stationary waves

Stationary Waves8

COMPREHENSIVE REVIEW

1. Stationary Waves

a) A wave, in which crests or troughs

(compressions or rarefactions) do not

change location in space, is called

stationary wave.

Like progressive waves, the stationarywaves can also be both transverse as wellas of longitudinal type and are formed bythe superposition of two progressive wavestravelling in opposite directions.

When two progressive waves, having

the same amplitude and period but

travelling in opposite directions with the

same velocity superimpose, a disturbance

that does not appear to travel in space is

obtained. Such a wave is called stationary

wave or standing wave.

Fig. 1.1

b) The stationary waves are represented asshown in fig. 1.1. Here waves are propagatingalong X-axis and the width of the loop atany point represents the amplitude (A

s) of

oscillations at that point. This shows that theamplitude of oscillations varies with distancealong the propagation of the wave.

c) The stationary waves are formed due to thesuperposition of a wave and its reflectedwave.

d) The points marked N in fig. 1.1 are callednodes. Here the amplitude of the oscillationis zero. And the points marked A are calledantinodes. Here, the amplitude of theparticles is maximum.

STATIONARY WAVES ( 180 )

2. Equation of stationary wave

Let the incident wave be :

1y Asin( t kx)

Its reflected wave will be :

2y Asin( t kx)

If the above mentioned incident and reflectedwaves superimpose, a stationary wave isproduced. The equation of the resultant stationarywave is :

1 2y y y 2A cos kx sin t

* In general, the equations for the stationary wavemay be written as follows :

y Acos kx sin t

y Asin kxsin t

y Acos kx cos t

y Asin kx cos t

a) The equation y 2A cos kx sin t satisfies

the differential equation,

2 2

2 2 2

d y 1 d y

dx c dt

where c .k

Hence, it is the equation of a

wave.

b) The amplitude of the stationary wave is :

sA 2A cos kx

The amplitude of the stationary wave is notconstant. It varies with x.

The point at which the amplitude is zero iscalled node and point at which the amplitudeis maximum is called antinode.

c) For node, we have sA 2A cos kx 0

Hence 3 5

kx , , ,....(2n 1) ,2 2 2 2

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where n = 0, 1, 3, .....

Since 2

k ,

hence for the node we have :

3 5x , , .....(2n 1)

4 4 4 4

d) The separation between the nodes is equal

to 2

.

e) For the antinodes, we have the amplitudemaximum and equal to 2A.

Hence cos kx 1. This gives,

kx 0, , 2 , 3 ,..... n

where n = 0, 1, 2, 3, .....

Since 2

k ,

therefore, we have

3 nx 0, , , ....

2 2 2

f) The separation between the two antinodes

is again .2

g) The separation between nodes & consecutive

antinode is 4

. See fig. 2.1.

Fig. 2.1

h) The amplitude of the stationary wave variesbetween 0 and 2A, where A is the amplitudeof the superimposing incident and reflectedwaves.

The velocity of the particle is given by,

dy d(2Acoskxsin t)

dt dt

2 A cos kx cos t

The maximum velocity depends on theposition of the particle. It is zero for theparticle at the nodes and largest for theparticles at the antinodes.

3. Characteristics of stationary waves

i) They do not propagate energy.

ii) All particles between the consecutive nodesvibrate in the same phase.

iii) Particles on the either side of the node vibratein opposite phase.

iv) Particles on the either side of the antinodevibrate in the same phase.

v) Particles at the nodes donot vibrate.

vi) The amplitude of SHM of the particlesincreases from node to antinode. It becomesmaximum at the antinode.

vii) The time period, frequency as well asangular frequency of the particles in thestationary wave is same as that of the incidentand the superposing reflected wave.

viii) In case of the longitudinal stationary wavethe pressure as well as density variationsare maximum at the node and minimum atthe antinode.

ix) The amplitude of SHM of the particles is afunction of position.

x) The phase of SHM of the particles is afunction of time.

xi) The strain is maximum at the nodes andminimum at the antinode.

xii) Energy associated with the SHM is maximumat the antinode and minimum at the node.

4. String

Is a thin, flexible thread or wire. Transversestationary vibration can be set up in a stretchedstring.

5. Organ pipe

Is a hollow tube having length much greaterthan its diameter. Longitudinal stationary vibrationscan be set up in the organ pipe.

If both ends are open, then we call it openorgan pipe.

If one end is closed, then we call it closedorgan pipe.





6. Note

Any musical sound produced by the simpleharmonic oscillations of the source is called note.

7. Tone

Every component of the musical sound iscalled tone. A note may consist of one or moretones.

8. Fundamental note & fundamental frequency

The note of lowest frequency produced byan instrument is called fundamental note. Thefrequency of this note is known as fundamentalfrequency.

9. Harmonics

If n be the frequency of fundamental noteproduced by an instrument, then the frequenciesn, 2n, 3n, 4n, ..... (integral multiples of n), whetheractually produced or not, are called harmonics.They are respectively termed as first, second, third,fourth harmonics.

10. Overtones

The harmonics other than the first (funda-mental note) which are actually produced by theinstrument are called overtones.

11. Octave

Is the frequency twice the fundamentalfrequency.

12. Modes of Vibration

The same musical instrument (string or organpipe) can produce a number of notes. Thevibrations corresponding to each note is calledmode. The mode of vibration corresponding tofirst harmonic is called fundamental mode.

13. Modes of vibration of a stretched string

The stationary waves are set up in thestretched string. The two fixed ends behave asnodes.

Fig. 13.1

i) The mode of vibration depends on theposition from which the string is plucked.

a) If we pluck the string from the middle(at x = /2, where x is the distance fromone of the fixed ends and = length ofthe string), then the string vibrates inthe fundamental mode producing thefirst harmonic.

b) If we pluck the string at x = /4, thestring vibrates in the 2nd mode producingthe second harmonic or the firstovertone.

c) If we pluck the string at x = /6 thestring vibrates in the 3rd mode producingthird harmonic or second overtone.

Fig. 13.2

Thus, the string vibrates in nth mode

when it is plucked at x .2n

In such

a case it produces nth harmonic and

(n 1)th overtone.

ii) The frequency of nth harmonic or (n 1)th

overtone of the string is given by :

n

n Tf

2

where T = tension in the string and is themass per unit length of the string.





iii) The wavelength for nth mode is given by :

n

2

n

iv)T

gives the velocity of the waves propa-

gating through the string.

v) That is, the frequency of the note emittedby a string is :

a) directly proportional to the number ofsegments (n) in which the string vibrates.

b) inversely proportional to the length of the string.

c) directly proportional to the square rootof tension (T) in the string.

d) inversely proportional to the squareroot of mass per unit length of thestring.

These are called laws of vibrationof the string.

vi) If D be the diameter of the string and bethe density of the material of the wire, then :

2D

4

Hence

1

21

2

n 2

1 T 1 Tf n 2

D2 2

4

or

1

2

p

1 Tf n

D

That is, the frequency of the notes emittedby the string is :

a) inversely proportional to the diameter(D) of the string.

b) inversely proportional to the squareroot of density of the wire.

These are called supplementary lawsof vibration of string.

14. Open organ pipe

Note. The modes of vibration of the open organpipe, the harmonics and the overtones producedby it are exactly similar to that of the stretchedstring.

The modes of vibration of the open organ

pipe are as shown below :

Fig. 14.1

i) The frequency of the various harmonics ofopen organ pipe are integral multiples of the

fundamental frequency.

ii) The frequency of the first overtone = 2 times

the frequency of the fundamental note andthat of second overtone = 3 times thefundamental frequency. Same is true forstring.

iii) In general, the frequency of the mth overtone= (m + 1) times the fundamental frequency.Same is true for string.

iv) All harmonics are present. That is, noharmonic is missing as is the case withclosed pipe.

v) Since the sound produced by open organpipe contains all harmonics, it is richer inquality than that produced by the closed

organ pipe.

vi) The frequency of the fundamental note of

an open organ pipe is double than that forclosed organ pipe of same length.

vii) At the open end the compression is reflectedas rarefaction and vice versa.

viii) In the open organ pipe, the number ofantinodes is one more than the number ofnodes.

ix) The open ends always act as antinode.





15. Closed organ pipe

The modes of vibration of the closed organ areas follows :

Fig. 15.1

i) The frequency of various overtones of theclosed organ pipe are odd integral multiplesof the fundamental frequency.

ii) The frequency of the first overtone = 3 timesthe frequency of the fundamental note andfrequency of the second overtone = 5 timesthe fundamental frequency.

iii) In general, frequency of the mth overtone =(2m + 1) times the fundamental frequency.

iv) The even harmonics (second, fourth, sixth

etc.) are missing.

v) The sound is poorer in quality than that ofopen organ pipe as even harmonics aremissing.

vi) The frequency of the fundamental note of aclosed organ pipe is half as compared to thatof an open pipe of the same length.

vii) At the closed end the compression isreflected as compression and rarefaction isreflected as rarefaction.

viii) The number of nodes in the closed organpipe is equal to the number of antinodes.

ix) The closed end always acts as node andthe open end acts as antinode.

16. End Correction

It is found that practically the antinode atthe open end of the organ pipe is not formedexactly at the open end. On the other hand, it isformed slightly away from the open end.

Generally we find that the antinode may beformed at a distance of x = 0.3 D away from theopen end.

Here, D = diameter of the tube.

Fig. 16.1

Therefore, the effective length of the closedorgan pipe is ' = + 0.3 D and that of the openorgan pipe is ' = + 0.6 D.

17. Resonance tube

The resonance tube is a closed organ pipewhose length can be changed say by changingthe water level in it. A vibrating tuning fork isplaced at the open end as shown in the figure.The tuning fork sets up longitudinal vibrations inthe air column. The first resonance occurs when

the length of the air column is 1 ,4

where

is the wavelength of the waves set up in the aircolumn.

Fig. 17.1

The frequency of these waves is same as that ofthe tuning fork say n. Then, if c be the velocity ofthe waves in air, then





1c n 4n

If end correction is taken into account, then :

1 0.3D4

... (i)

Hence c 4n( 0.3D) ... (ii)

Second resonance

The second resonance occurs when 2

3,

4

Taking the end correction into account, we find :

2

30.3D

4

... (iii)

Hence 2

4( 0.3D)

3

And 2

4c n( 0.3D)

3 ... (iv)

From equations (i) and (iii), we find :

2 12

Hence, 2 1c 2n[ ]

* Thus, by using the first and second resonance,the end correction can be eliminated.





Stationary Waves and its Equation

1. Which of the following statements is correct aboutthe stationary waves ?

a) All the particles of the medium vibrate in thesame phase

b) Particles at the consecutive antinodes differin phase by

c) Particles at the consecutive antinodes are insame phase

d) The phase lag between the particles continuouslyvaries with increase in distance

2. Two waves each of loudness L superimpose toproduce beats. The maximum loudness of thebeats will be :

a) L b) 2 L

c) 4 L d) none of the above

3. Which of the following expressions representssimple harmonic stationary wave ?

a) A sin t Bcos t

b) A sin t Bcos kx

c) Asin t cos kx d) Asin( t kx)

4. The equation of stationary wave is,

xy 4sin cos(100 t)

5

where y and x are in metres and 1 is in seconds.In Q.4 the amplitude of the progressive wave thatproduce the stationary wave is :

a) 1 m b) 2 m

c) 4 m d) 8 m

5. In Q.4 the wavelength of the progressive wavethat produce the stationary wave is :

a) m b) 2 m

c) 5

m d) none of the above

6. In Q.4 the velocity of the progressive wave is :

a) 10 ms–1 b) 50 ms–1

c) 100 ms–1 d) 500 ms–1

7. In Q.4 the frequency of the progressive waveis :

a) 10 Hz b) 50 Hz

c) 100 Hz d) 500 Hz

MULTIPLE CHOICE QUESTIONS

8. In Q.4 the distance between consecutive nodesis :

a) 2 m b) 4 m

c) 5 m d) 10 m

9. Two waves of intensities and 4 superimpose.The minimum and maximum intensities willrespectively be :

a) 3, 5 b) , 5

c) , 9 d) none of the above

10. The ratio of intensities of two waves is 1 : 16.The ratio of their amplitude is :

a) 1

4b)

1

2

c) 1

16d)

16

17

11. In the equation of simple harmonic wave

y 0.6sin(0.3t 0.2), the initial phase is :

a) 0.3 t b) 0.3

c) 0.2 d) (0.35 t + 0.2)

12. Which of the following characteristics of thesound wave are affected by the change intemperature ?

a) Wavelength b) Frequency

c) Amplitude d) Intensity

13. Surface waves strike the rock with their crests160 m apart. The velocity of the waves is 40 ms–1.The time interval between the two crests strikingthe rock is :

a) 1 s b) 2 s

c) 4 s d) 8 s

14. If I0 be the threshold intensity of hearing, then

what will be the corresponding pressure amplitudeof sound wave in air of density and soundspeed c ?

a) 02 I c b) 02 I c

c) 0I c d) 0I c

15. If I1 and I

2 be two intensities of sound and L

1 and

L2 be the corresponding loudnesses,

then 2

1

Ilog

I





a) 2

1

L

L b) L2 – L

1

c) L2 L

1d) L

2 + L

1

Vibration of String

16. In case of vibrating string, the frequency of thefirst overtone is equal to frequency of the :

a) fundamental note

b) first harmonic

c) second harmonic

d) none of the above

17. For two systems to be in resonance, which of thefollowing properties should be equal ?

a) Wavelength b) Frequency

c) Amplitude d) Wave velocity

18. The string of a sonometer is plucked so as tomake it vibrate in one segment. The soundproduced is called :

a) first harmonic b) first overtone

c) second harmonic d) second overtone

19. What types of waves are produced in the sonometerwire ?

a) Transverse and progressive

b) Transverse and stationary

c) Longitudinal and progressive

d) Longitudinal and stationary

20. Stationary waves are set up between the ends ofa string 2 m long. It vibrates in 4 segments. Thedistance between consecutive nodes is :

a) 50 cm b) 1 m

c) 1.4 m d) 2 m

21. The sound of minimum frequency emitted by avibrating string is NOT termed as :

a) first overtone b) first harmonic

c) fundamental tone

d) none of these

22. If tension in the string is increased from 1 kN to4 kN, other factors remaining unchanged, thefrequency of the second harmonic will :

a) be halved

b) remain unchanged

c) be doubled

d) become four times

23. Both length and diameter of the stretched stringare doubled. If earlier the frequency of thefundamental note was n, now the frequency willbe equal to :

a) 4 n b) n

c) n

4d) none of the above

24. Both the stretching force and diameter of thestretched string are doubled. If earlier thefrequency of the fundamental note was n, nowthe same will be equal to :

a) 4 n b) n

c) n


25. What is the nature of the transverse wavesproduced on the stretched string ?

a) Stationary and polarised

b) Progressive and polarised

c) Stationary and unpolarised

d) Progressive and unpolarised

26. The frequency of the first harmonic emitted by astring is 100 Hz. The frequency of the third overtonewill be :

a) 200 Hz b) 300 Hz

c) 400 Hz d) 500 Hz

27. The speed of mechanical longitudinal waves inbrass is 3500 ms–1. A brass rod is clamped at oneend. If the length of the rod is 70 cm, the frequencyof fundamental note produced by it will be :

a) 35 Hz b) 70 Hz

c) 700 Hz d) none of the above

28. A rod 70 cm long is clamped from middle. Thevelocity of sound in the material of the rod is3500 ms–1. The frequency of fundamental noteproduced by it is :

a) 700 Hz b) 1250 Hz

c) 2500 Hz d) 3500 Hz

29. Fundamental frequency of a sonometer wire isn. If its length, diameter as well as tension aredoubled, the new fundamental frequency will be :

a) n b) 2n

c) n

2d)

n

2 2





30. If we add 8 kg load to the hanger of sonometer,the fundamental frequency becomes 3 times ofits initial value. The initial load in the hanger was :

a) 0.5 kg wt b) 1 kg wt

c) 2 kg wt d) 4 kg wt

31. Two tuning forks when sounded together produce5 beats per second. The first tuning fork is inresonance with 16.0 cm wire of a sonometer andthe second is in resonance with 16.2 cm wire ofthe same sonometer. The frequencies of the tuningforks are :

a) 100 Hz, 105 Hz b) 200 Hz, 205 Hz

c) 300 Hz, 305 Hz d) 400 Hz, 405 Hz

32. A tuning fork produces 5 beats with sonometerwires of 40 cm as well as 44 cm, other factorsremaining unchanged. The frequency of the tuningfork is :

a) 80 Hz b) 88 Hz

c) 105 Hz d) 160 Hz

33. The tension in a wire is decreased by 19%. Thepercentage decrease in frequency will be :

a) 0.19 % b) 10 %

c) 19 % d) none of the above

34. The string of a sonometer is divided into two partswith the help of a wedge. The total length of thestring is 1 m and the two parts differ in length by2 mm. When sounded together, they produced twobeats. The frequencies of the notes emitted bythe two parts are :

a) 499 and 497 b) 501 and 499

c) 501 and 503 d) none of the above

35. Two stretched wire of same length, diameter andsame material are in unison. The tension in one isincreased by 2% and 2 beats per second areheard. What was the frequency of the note producedwhen they were in unison ?

a) 100 Hz b) 200 Hz

c) 300 Hz d) 400 Hz

36. A stretched string is 1 m long. Its mass per unitlength is 0.5 gm–1. It is stretched with a force of20N. If plucked at a distance of 25 cm from oneend, the frequency of the note emitted by it willbe :

a) 100 Hz b) 200 Hz

c) 300 Hz d) 400 Hz

37. Beats are produced due to the superposition oftwo progressive notes. Maximum loudness at thewaxing is n times the loudness of either notes.What is the value of n ?

a) 1 b) 2

c) 2 d) 4

38. Two waves each of loudness L superimpose toproduce beats. The maximum loudness of thebeats will be :

a) L b) 2 L

c) 4 L d) none of the above

39. A piano wire having a diameter of 0.90 mm isreplaced by another wire of the same materialbut with a diameter of 0.93 mm. If the tension ofthe wire is kept the same, then the percentagechange in the frequency of the fundamental toneis :

a) + 3 % b) + 3.2 %

c) – 3.2 % d) – 3 %

40. A stretched string of length fixed at both endscan sustain stationary waves of wavelength given by :

a) 2n

2

b)

2

2n

c) 2

n

d)

2

n

41. Four wires of identical lengths, diameters andmaterials are stretched on a sonometer box. Theratio of their tensions is 1 : 4 : 9 : 16. The ratio oftheir fundamental frequencies is :

a) 16 : 9 : 4 : 1 b) 4 : 3 : 2 : 1

c) 1 : 2 : 3 : 4 d) 1 : 4 : 9 : 16

42. The distance between two consecutive nodes ona stretched string is 10 cm, It is in resonance witha tuning fork of frequency 256 Hz. What is thevelocity of the progressive wave in the string ?

a) 51.20 ms–1 b) 25.60 ms–1

c) 12.80 ms–1 d) 6.40 ms–1

43. A sonometer wire is to be divided into threesegments having fundamental frequencies in theratio 1 : 2 : 3. What should be the ratio of theirlengths ?

a) 6 : 3 : 2 b) 4 : 3 : 2

c) 4 : 2 : 1 d) 3 : 2 : 1





44. What is the phase difference between theparticles of a string on the sides of antinode ?

a) 00 b) 450

c) 900 d) 1800

45. What is the phase difference between the particlesof a string on the sides of antinode ?

a) 00 b) 450

c) 900 d) 1800

46. A tuning fork of frequency 340 Hz produces 5beats per second with a sonometer wire. If thetension is slightly increased, the number of beatsbecomes 4. What is the frequency of the sonometerwire ?

a) 335 Hz b) 345 Hz

c) 330 Hz d) 350 Hz

Closed Organ Pipe

47. The frequency of the fundamental note producedby closed organ pipe is n. If the diameter of thepipe is doubled, the frequency of the fundamentalnote produced by it will be :

a) 4 n b) 2 n

c) n d) n

2

48. The frequency of the third harmonic of a closedorgan pipe is equal to which of the followingovertones ?

a) First b) Second

c) Third d) None of the above

49. The fundamental note produced by a closed organpipe is of frequency f. The fundamental noteproduced by an open organ pipe of same lengthwill be of frequency :

a) 2 f b) f

c) f


50. The first overtone produced by a closed organpipe is of frequency f. The first overtone producedby an open organ pipe of same length will be offrequency :

a) 2 f b) f

c) f


51. In case of closed organ pipe which harmonic thepth overtone will be ?

a) 2p + 1 b) 2p – 1

c) p + 1 d) p – 1

52. In a closed organ pipe, the frequency of thefundamental note is 50 Hz. The note of which ofthe following frequencies will not be emitted byit ?

a) 50 Hz b) 100 Hz


53. In a closed. organ pipe, the fundamental frequencyis 50 Hz. The frequency of second overtone is :

a) 100 Hz b) 150 Hz

c) 200 Hz d) 250 Hz

54. The velocity of sound in air is 320 ms–1. A closedorgan pipe of length 20 cm resonates at a frequencyof 1200 Hz. Which overtone is it ?

a) 1st b) 2nd

c) 3rd d) 4th

55. Two closed organ pipes, when sounded togethergive five beats per second. Their lengths are inthe ratio of 100 : 101. The fundamental notes (inHz) produced by then are :

a) 245, 250 b) 250, 255

c) 495, 500 d) 500, 505

56. Given that the velocity of sound in air is 320 ms–1.At which one of the following frequencies, a pipeclosed at one end can resonate, if its length is1 m ?

a) 40 Hz b) 160 Hz

c) 320 Hz d) 400 Hz

57. A cylindrical tube open at both ends producesfundamental note of frequencies 256 Hz. The tubeis dipped vertically in water so that half of it is inwater. The air column in tube will be in (first)resonance with a tuning fork of frequency :

a) 128 Hz b) 256 Hz


58. The shortest length of air column in a tube, openat both ends, that resonates with a tuning fork is16 cm. At what length will the second resonanceoccur in such a tube with the same tuning fork ?

a) 24 cm b) 32 cm

c) 40 cm d) none of the above





59. The shortest length of air column in a tube, closedat one end, that resonates with a tuning fork is16 cm. At what length of the air column will thesecond resonance occur in such a tube with thesame tuning fork ?

a) 24 cm b) 32 cm

c) 40 cm d) none of the above

60. A vibrating tuning fork of frequency 480 Hz isheld at the mouth of a resonance column ofresonant frequency 484 Hz. What is the numberof beats produced ?

a) 8 b) 4

c) 2 d) zero

Open Organ pipe

61. In open organ pipe which harmonics are missing ?

a) Odd b) Even

c) None

d) Depends upon length of the pipe

62. In open organ pipe, first overtone produced is ofsuch a frequency that length of the pipe is equalto :

a) 4

b)

2

c) 3

d)

63. In case of open organ pipe which harmonic thepth overtone will be ?

a) 2p + 1 b) 2p – 1

c) p + 1 d) p – 1

64. What happens to the frequency of the noteproduced by an organ pipe when its diameter isincreased keeping the length unchanged ?

a) Increases

b) Decreases

c) Remains unchanged

d) Increases for open pipe and decreases for theclosed pipe

65. The velocity of sound in air is 320 ms–1. An openorgan pipe of length 40 cm long resonates at afrequency of 1200 Hz. Which overtone is it ?

a) 1st b) 2nd

c) 3rd d) 4th

66. A tube closed at one end and containing airproduces fundamental note of frequency of256 Hz. If the tube is open at both ends, thefundamental frequency will be :

a) 64 Hz b) 128 Hz

c) 384 Hz d) 512 Hz

67. An organ pipe P1 closed at one end vibrating in

its first harmonic and pipe P2 open at both ends

vibrating in its third harmonic are in resonancewith the same tuning fork. The ratio of their lengthis :

a) 1

8b)

1

6

c) 3

4d)

3

8

68. The frequency of the first overtone of an openorgan pipe is same as that of the closed organpipe. If the length of the open organ pipe is L,then that of the closed organ pipe will be :

a) L

4b)

L

2

c) 3L

4d) L

69. An organ pipe P1 closed at one end vibrating in

its first harmonic and another pipe P2 open at

both ends vibrating in its third harmonic are inresonance with a given tuning fork. The ratio ofthe length of P

1 to that of P

2 is :

a) 1

8b)

1

6

c) 1

4d)

1

2

70. A cylindrical tube, open at both ends, has afundamental frequency f in air. The tube is dippedvertically in water so that half of it is in water.The fundamental frequency of the air column isnow :

a) f

2b)

3f

4

c) f d) 2 f

71. An open organ pipe of length 50 cm vibrates inunison with a tuning forks of frequency f. Thediameter of the pipe is 3 cm. What is the wavelengthof the note produced ?





a) 52 cm b) 96 cm

c) 104 cm d) 204 cm

72. In the above case if the organ pipe is closed atone end, the wavelength will be :

a) 52 cm b) 96 cm

d) 104 cm d) 204 cm

73. A hollow metallic tube of length and open atboth ends is in resonance with a tuning fork offrequency f. If one end of the tube is immersed

in water upto a length ,2

it will resonate with a

tuning fork of frequency :

a) 2 f b) 2f

c) f d) f

2

74. Frequency of an open organ pipe is 300 Hz. Thefirst overtone of this pipe is same as the firstovertone of a closed organ pipe. What is the lengthof closed organ pipe ? The speed of sound is336 m/s :

a) 11 cm b) 21 cm

c) 42 cm d) 84 cm

Free and Forced Vibrations, Resonance

75. When we speak into a microphone, what typesof vibrations the diaphragm executes ?

a) Free b) Forced

c) Resonant d) None of the above

76. A vibrating tuning fork is placed close to anotherof equal frequency. The other also starts vibrating.This happens because of :

a) superposition

b) formation of stationary waves

c) interference d) resonance

77. Which of the following can be used to determinethe velocity of sound in solids, liquids as well asgases ?

a) Organ pipe b) Sonometer

c) Kundt's tube d) Resonance tube

78. A sonometer is in resonance with a tuning fork.The maximum intensity of the sound is I and itlasts for time t. If the box of the sonometer isevacuated, which of the following is true ?

a) Both I and t increase

b) Both I and t decrease

c) I decreases and t increases

d) I increases and t decreases

79. In a resonance column the first resonance occursat 16 cm and the second resonance occurs at49 cm. If the velocity of sound in air be 300 ms–1,the frequency of the tuning fork with whichresonance occurs will be :

a) 500 Hz b) 330 Hz

c) 250 Hz d) 165 Hz

80. In a resonance tube the first resonance occurs at16 cm and the second resonance occurs at 49 cm.The end corrections will be :

a) 0.3 cm b) 0.5 cm

c) 0.8 cm d) 1.0 cm

Recent Questions from MH-CET Exams

81. The frequency of the third overtone of a closedpipe of length

c is the same as the frequency of

the sixth overtone of an open pipe of the length

0, Then :

a) 0

c

1

2

b)

0

c

2

c) 0

c

1

4

d)

0

c

4

82. The resultant amplitude of a stationary wave is :

a) constant

b) varies periodically with distance x

c) varies periodically with both x and t

d) varies periodically with time t

83. The frequency of the fundamental mode ofvibration of a stretched string of length '' , lineardensity 'm' and subjected to a tension 'T' is :

a) T b)1

T

c)

d) independent of T and m

84. What happens to natural frequency of vibrationof a stretched wire when its length and diameterare increased ?





a) No change in the frequency takes place

b) Frequency decreases

c) Frequency increases

d) May increase or decrease

85. A tuning fork of 256 Hz is held over an emptymeasuring cylinder. Water is slowly poured intoan air column of length 0.33 m. The speed ofsound in air, to a first approximation is 338 m/s.This is less than the actual value because :

a) measuring cylinder is used as a resonance tube

b) measuring cylinders are not made of metals

c) displacement antinode at /4 actually liesoutside the top of the cylinder

d) as water is poured, it was the third harmonicthat was heard

86. The tension in the sonometer wire is increasedby 21%. Its fundamental frequency :

a) increases by 21% b) increases by 10%

c) increases by 5% d) increases by 7%

87. A standing wave having 3 nodes and 2 antinodesis formed between two atoms having a distanceof 1.21 Å between them the wavelength ofstanding wave will be :

a) 3.63 Å b) 6.05 Å

c) 1.21 Å d) 2.42 Å

88. Two closed pipe produce 10 beats per secondwhen emitting their fundamental nodes. If theirlength are in ratio of 25 : 26 their fundamentalfrequency in Hz are :

a) 270, 280 b) 260, 270

c) 260, 250 d) 260, 270

89. Transverse position in Melde's experiment ischanged to parallel position, if length of stringremaining the same and tension is made half. Ifin perpendicular position 4 loops are formed, no.of loops formed in parallel position :

a) 1 b) 2

c) 3 d) 4

90. In a pipe open at both ends distance betweennode and antinode is :

a) 4

b)

2

c) 3

2

d) none of these

91. The harmonics which are present in a pipe openat one end are :

a) odd harmonics

b) even harmonics

c) even as well as odd harmonics

d) none of these

92. In Melde's experiment, the string vibrates in 4loops when a 50 gram weight is placed in the panof weight 15 gram. To make the string to vibratein 6 loops the weight that has to be removed fromthe pan is :

a) 0.0007 kg wt b) 0.0021 kg wt

c) 0.0036 kg wt d) 0.0029 kg wt

93. For a closed organ pipe resonance is occuredwhen air columns of lengths are equal to :

a) , ,4 2

b)

3 5, ,

2 2 2

c) , ,32

d)

3 5, ,

4 4 4

94. A string is vibrating in first overtone, then pointformed exactly at the middle is :

a) node

b) antinode

c) sometimes node and sometimes anti node

d) none of these

95. The fundamental frequency of a closed pipe, ifits first overtone is unison with a tuning fork of480 Hz, is :

a) 120 Hz b) 320 Hz

c) 160 Hz d) 240 Hz

96. Fifth overtone of closed organ pipe is unision withfifth overtone of open organ pipe. The ratio oftheir length is :

a) 12

11b)

11

12

c) 5

6d)

6

5

97. A pipe, of length 10 cm, closed at one, hasfrequency equal to half the 2nd overtone of anotherpipe open at both the ends. The length of the openpipe is :

a) 30 cm b) 40 cm

c) 20 cm d) 10 cm





98. If the mass of empty pan in Meldes' s experimentis m

0, when m

1 mass is kept in it, the number of

loops are found to be p1. When mass m

2 is added

in the pan a number of loops are p2. Both the

arrangements are in transverse position. Then themass of empty pan in terms of p

1, p

2, m

1 and m

2

is :

a)

2 21 2 2 1

2 21 2

(m p m p )

(p p )

b)

2 22 2 1 1

2 21 2

(m p m p )

(p p )

c)

2 21 22 2

2 2 1 1

(p p )

(m p m p )

d)

2 22 12 2

1 2 1 1

(p p )

(m p m p )

99. A stationary wave incident on rigid wall. Thenthe distance between wall and first antinode is :

[Velocity of wave is 36 m/s and frequency 72 Hz]

a) 1

m2

b) 1

m4

c) 1

m8

d) 1 m

100. The frequency of open organ pipe is :

a) v

2 0.4db)

v

2 0.6d

c) v

2 0.8dd)

v

2 1.2d

101. y = 3 cos 100 (2t – x). The value of is :

a) 4 cm b) 6 cm

c) 2 cm d) 1 cm

102. In the fundamental mode, time taken by the waveto reach the closed end of the air filled pipe is0.01 s. The fundamental frequency is :

a) 25 b) 12.5

c) 20 d) 15

103. n1 is the frequency of the pipe closed at one end

and n2 is the frequency of the pipe open at both

ends. If both are joined end to end, find thefundamental frequency of closed pipe so formed :

a) 1 2

2 1

n n

n 2n b) 1 2

2 1

n n

3n n

c) 1 2

2 1

n 2n

n n

d)

1 2

2 1

2n n

n n

104. The tension of a stretched string is increased by69%. In order to keep its frequency of vibrationconstant, its length must be increased by :

a) 20 % b) 20 %

c) 69 % d) 69 %

105. Keeping the length of the pipe constant if diameterof the pipe increased twice, then frequency ofpipe will :

a) slightly increase

b) slightly decrease

c) remain constant

d) increase four times

106. If the frequency of first harmonic of a closedpipe, is in unison with the third harmonic of openpipe. Then the ratio of lengths of the pipe closedat one end to the open at both the ends is :

a) 1

12b)

3

4

c) 1

6d)

6

7

107. If oil of density higher than that of water is usedin place of water in a resonance tube, its frequencywill be :

a) decrease b) increase

c) remain the same d) can not say

108. The string stretched by tension T length L vibrateswith fundamental frequency n. The tension in thestretched string is increased by 69% and lengthof the string reduces by 35%. Then the frequencyof vibrating string is :

a) n b) 1.5 n

c) 2 n d) n

2

109. In sonometer experiment, the bridges are separatedby a fixed distance. The wire which is slightlyelastic, emits a tone of frequency 'n' when heldby tension 'T'. If the tension is increased to '4T',the tone emitted by the wire will be of frequency :

a) n

b) 2 n

c) Slightly greater than 2 n

d) Slightly less than 2 n





110. An open and closed organ pipe have the samelength. The ratio of 'p'th mode of frequency ofvibration of air in two pipes is :

a) p(2p 1) b) 2p

2p 1

c) p d) 1

111. In a pipe open at both ends, 'n1' and 'n

2' be the

frequencies corresponding to vibrating lengths '1'

and '2' respectively. The end correction is :

a) 1 1 2 2

1 2

n n

2(n n )

b) 2 2 1 1

2 1

n n

2(n n )

c) 2 2 1 1

1 2

n n

2(n n )

d) 1 1 2 2

1 2

n n

(n n )

112. The length and diameter of a metal wire is doubled.The fundamental frequency of vibration willchange from 'n' to (Tension being kept constantand material of both the wires is same) :

a) n

4b)

n

8

c) n

12d)

n

16

REVISION OUESTIONS

from Competitive Exams

1. For a resonance tube the air columns for the firstand the second resonance differ in length by31.5 cm. The wave length of the sound wave is :

a) 31.5 cm b) 63.0 cm

c) 126.0 cm d) 252.0 cm

2. A stretched string of one metre length, fixed atboth ends, having a mass of 5 10–4 kg is undera tension of 20 newton. It is plucked at a pointsituated at 25 cm from one end. The stretchedstring would vibrate with a frequency of :

a) 400 Hz b) 100 Hz

c) 200 Hz d) 256 Hz

3. The fundamental frequency of a string stretchedwith a weight of 4 kg is 256 Hz. The weightrequired to produce its octave is :

a) 4 kg wt b) 12 kg wt

c) 16 kg wt d) 24 kg wt

4. The intensity of sound wave while passing throughan elastic medium falls down by 10% as it coversone metre distance through the medium. If theinitial intensity of the sound wave was 100decibels, its value after it has passed through3 metre thickness of the medium will be :

a) 70 decibel b) 72.9 decibel

c) 81 decibel d) 60 decibel

5. A sonometer wire is in unison with a tuning fork.Keeping the same tension, the length of the wirebetween the bridges is doubled. The tuning forkcan still be in resonance with the wire, providedthe wire now vibrates in :

a) 4 segments b) 6 segments

c) 3 segments d) 2 segments

6. A travelling wave passes a point of observation.At this point the time interval between successivecrests is 0.2 second :

a) wavelength is 5 metre

b) frequency is 5 Hz

c) velocity of propogation is 5 ms–1

d) wavelength is 0.2 metre

7. A tuning fork and a sonometer wire soundedtogether produce 4 beats per second when thelength of the wire is 95 cm or 100 cm. The frequencyof the tuning fork is :





a) 156 b) 152

c) 148 d) 160

8. Two wires of the same material and radii r and2r respectively are welded together end to end.The combination is used as a sonometer wire andkept under tension T. The welded point is mid-way between the two bridges. When stationarywaves are set up in the composite wire, the jointis a node. Then the ratio of the number of loopsformed in the thinner to thicker wire is :

a) 2 : 3 b) 1 : 2

c) 2 : 1 d) 5 : 4

9. A wave is represented by the equation,

y Asin 10 x 15 t ,3

where x is in

metres and t is in seconds. The expressionrepresents :

a) a wave travelling in the positive X directionwith a velocity of 1.5 ms–1

b) a wave travelling in the negative X directionwith a velocity of 1.5 ms–1

c) a wave travelling in the negative X directionwith a wavelength of 0.2 metre

d) a wave travelling in the positive X directionwith a wavelength of 0.2 metre

10. The equation of stationary wave along a stretchedstring is given by,

xy 5sin cos40 t,

3

where x and y are in

centimetres and t in seconds. The separationbetween two adjacent nodes is :

a) 1.5 cm b) 3 cm

c) 6 cm d) 4 cm

11. The distance between two consecutive crests ina wave train produced in a string is 5 cm. If 2complete waves pass through any point persecond, the velocity of the wave is :

a) 10 cm/s b) 2.5 cm/s

c) 5 cm/s d) 15 cm/s

12. Velocity of sound waves in air is 330 metre persecond. For a particular sound in air, a path differenceof 40 cm is equivalent to a phase difference of1.6 . The frequency of this wave is :

a) 165 Hz b) 150 Hz

c) 660 Hz d) 330 Hz

13. The speed of sound in air is 350 metre per second.The fundamental frequency of an open pipe 50 cmlong will be :

a) 175 Hz b) 350 Hz

c) 700 Hz d) 50 Hz

14. A tuning fork of frequency 480 Hz produces10 beats per second when sounded with avibrating sonometer string. What must have beenthe frequency of the string if a slight increase inthe tension of the string produced fewer beatsthan before ?

a) 460 Hz b) 470 Hz

c) 480 Hz d) 490 Hz

15. A closed organ pipe and an open organ pipe havetheir first overtone identical in frequency. Theirlengths are in the ratio :

a) 1 : 2 b) 3 : 4

c) 2 : 3 d) 4 : 5

16. Two sources of sound are said to be coherent if :

a) they produce sounds of equal intensity

b) they produce sounds of equal frequency

c) they produce sound waves vibrating with thesame phase

d) they produce sound waves with zero orconstant phase difference at all instants of time

17. A stretched string resonates with tuning fork offrequency 512 Hz when length of the string is0.5 m. The length of the string required to vibrateresonantly with a tuning fork of frequency 256 Hzwould be :

a) 0.25 m b) 0.5 m

c) 1 m d) 2 m

18. For production of beats the two sources musthave :

a) different frequencies and same amplitude

b) different frequencies

c) different frequencies, same amplitude andsame phase

d) different frequencies and same phase

19. A glass tube of 1.0 m length is filled with water.The water can be drained out slowly at the bottomof the tube. If a vibrating tuning fork of frequency500 c/s is brought at the upper end of the tubeand the velocity of sound is 330 m/s, then thetotal number of resonances obtained will be :





a) 4 b) 3

c) 2 d) 1

20. A standing wave is represented by,

Y Asin(100 t) cos(0.01 x),

where Y and A are in rnillimetre, t in seconds andx is in metre. Velocity of wave is :

a) 104 m/s b) 1 m/s

c) 10–4 m/s

d) not derivable from above data

21. A wave of frequency 100 Hz is sent along a stringtowards a fixed end. When this wave travels backafter reflection, a node is formed at a distance of10 cm from the fixed end of the string. The speedof incident (and reflected) wave is :

a) 40 m/s b) 20 m/s

c) 10 m/s d) 5 m/s

22. When an open organ pipe is sounded with a tuningfork having frequency 256 Hz resonance occuredat 35 cm and 105 cm, the velocity of sound is :

a) 360 m/s b) 512 m/s

c) 524 m/s d) all of these

23. A weight is attached to the free end of a sonometerwire. It gives resonance at a length of 40 cm whenit is resonanced with a tuning fork of frequency512. The weight is then immersed wholly in water,the resonant length is reduced to 30 cm. The relativedensity of the fluid in which weight is suspendedis :

a) 16

9b)

16

7

c) 16

5d)

16

3

24. At a certain instant a stationary transverse waveis found to have maximum kinetic energy. Theappearance of string at that instant is :

a) sinusoidal shape with amplitude A/3

b) sinusoidal shape with amplitude A/2

c) sinusoidal shape with amplitude A

d) straight line

25. Two open organ pipes of length 50 cm and 50.5 cmproduce 0.3 beats/sec, then the velocity of soundis :

a) 300 m/sec b) 30 m/sec

c) 303 m/sec d) none of these

26. In stationary wave the strain is :

a) Maximum at nodes

b) Maximum at antinode

c) Constant throughout

d) None of the above

27. The frequency of an open organ pipe is f. If halfpart of organ pipe is dipped in water then itsfrequency is :

a) f b) 3f

4

c) f

2d) 0

28. The length of a sonometer wire AB is 100 cm.Where should the two bridges be placed from Ato divide the wire in 3 segments whose fundamentalfrequencies are in the ratio of 1 : 2 : 3 ?

a) 30 cm, 90 cm b) 60 cm, 90 cm

c) 40 cm, 80 cm d) none of these

29. A source of sound gives five beats per second,when sounded with another source of frequency100 s–1. The second harmonic of the source,together with a source of frequency 205 s–1 givesfive beats per second. What is the frequency ofthe source ?

a) 105 s–1 b) 205 s–1

c) 95 s–1 d) 100 s–1

30. A toothed wheel is rotated at 120 r.p.m. and apost-card is placed against the teeth. How manyteeth (frequency) must the wheel have to producea note whose pitch is same as that of a tuningfork of frequency 256 /second ?

a) 120 256 b) 120

c) 256 d) 128

31. The couple of tuning forks produces 2 beats inthe time interval of 0.4 seconds so the beatfrequency is :

a) 8 Hz b) 5 Hz

c) 2 Hz d) 8 Hz

32. The distance between node and anti-node is :

a) b) 2

c) 4

d) 2





33. The air column in a pipe which is closed at oneend will be in resonance with a vibrating tuningfork at a frequency 260 Hz, if the length of theair column is :

a) 31.73 cm b) 62.5 cm

c) 35.75 cm d) 12.5 cm

34. A 1 cm long string vibrates with fundamentalfrequency of 256 Hz. If the length is reduced to

1cm

4 keeping the tension unaltered the new

fundamental frequency will be :

a) 64 b) 256

c) 512 d) 1024

35. A cylindrical resonance tube, open at both ends,has a fundamental frequency, F in air. If half ofthe length is dipped vertically in water, thefundamental frequency of the air column will be :

a) F

2b) F

c) 3F

2d) 2 F

36. Standing waves are produced in a 10 m longstretched string. If the string vibrates in 5segments and the wave velocity is 20 m/s, thefrequency is :

a) 2 Hz b) 4 Hz

c) 5 Hz d) 10 Hz

37. If velocity of sound in air be 350 m/s then thefundamental frequency of a open pipe of length50 cm is :

a) 175 Hz b) 350 Hz

c) 700 Hz d) 500 Hz

38. y = a cos (kx + t) superimposes on another wavegiving a stationary wave having node at x = 0.What is the equation of the other wave ?

a) – a cos (kx + t)

b) a cos (kx – t)

c) – a cos (kx – t)

d) – a sin (kx + t)

39. A tuning fork makes 256 vibrations per second inair. When the velocity of sound is 330 m/s, thenwavelength of the tone emitted is :

a) 0.56 m b) 0.89 m

c) 1.11 m d) 1.29 m

40. Velocity of sound in air is 320 ms–1. A pipe closedat one end has a length of 1 m. Neglecting end-corrections, the air column in the pipe can notresonate for sound of frequency :

a) 80 Hz b) 240 Hz

c) 320 Hz d) 400 Hz

41. Equation of a stationary wave is,

xy 4sin cos40 t

3

Then the separation between two consecutivenodes is :

a) 12 b) 3

c) 6 d) 1.5

42. In the production of beats by 2 waves of sameamplitude and nearly same frequency, themaximum intensity of each of the constituentwaves is :

a) same b) 2 times

c) 4 times d) 8 times

43. A rod is fixed between 2 points and is vibrating.The length of the rod for the first harmonic willbe :

a) b) 2

c) 2 d) 4

44. If n1, n

2 and n

3 are the fundamental frequencies

of three segments into which a string is divided,then the original fundamental frequency n of thestring is given by :

a)1 2 3

1 1 1 1

n n n n

b) 1 2 3n n n n

c)1 2 3

1 1 1 1

n n n n

d) 1 2 3n n n n

45. When a string is divided into three segments oflength

1,

2 and

3 the fundamental frequencies

of these three segments are v1, v

2 & v

3 respectively.

The original fundamental frequency (v) of thestring is :





a) 1 2 3v v v v

b) 1 2 3v v v v

c)1 2 3

1 1 1 1

v v v v

d)1 2 3

1 1 1 1

v v v v

46. A cylindrical tube, open at both ends, has afundamental frequency, f, in air. The tube is dippedvertically in water so that half of it is in water.The fundamental frequency of the air-column isnow :

a) 2 f b) f

c) f

2d)

3f

4

47. A sonometer wire of length 1.5 m is made of steel.The tension in it produces an elastic strain of 1%.What is, the fundamental frequency of steel ifdensity and elasticity of steel are 7.7 103 kg/m3

and 2.2 1011 N/m2 respectively ?

a) 770 Hz b) 188.5 Hz

c) 178.2 Hz d) 200.5 Hz

48. A horizontal stretched string, fixed at two ends,is vibrating in its fifth harmonic according to theequation,

(x, t) = (0.01 m) sin [(62.8 m–1) x]

cos [(628 s–1) t].

Assuming = 3.14, the correct statement(s) is(are) :

a) The number of nodes is 5

b) Then length of the string is 0.25 m

c) The maximum displacement of the midpointof the string, from its equilibrium position is0.01 m

d) The fundamental frequency is 100 Hz

49. If n1, n

2 and n

3 are the fundamental frequencies

of three segments into which a string is divided,then the original fundamental frequency n of thestring is given by :

a) 1 2 3n n n n

b)1 2 3

1 1 1 1

n n n n

c)1 2 3

1 1 1 1

n n n n

d) 1 2 3n n n n

50. The number of possible natural oscillations of aircolumn in a pipe closed at one end of length 85 cmwhose frequencies lie below 1250 Hz are :

[Velocity of sound = 340 ms–1]

a) 6 b) 4

c) 5 d) 7

51. A pipe of length 85 cm is closed from one end.Find the number of possible natural oscillationsof air column in the pipe whose frequencies liebelow 1250 Hz. The velocity of sound in air is340 m/s :

a) 12 b) 8

c) 6 d) 4

52. A student is performing an experiment using aresonance column and a tuning fork of frequency244 s–1. He is told that the air in the tube has beenreplaced by another gas (assume that the columnremains filled with the gas). If the minimum heightat which resonance occurs is (0.350 ± 0.005)m,the gas in the tube is :

Useful information :

1/ 2 1/ 2167RT 640 J mole

1/ 2 1/ 2140RT 590 J mole

The molar masses M in grams are given in the

options. Take the values of 10

M for each gas as

given there :

a) Neon 10 7

M 20, 20 10

b) Nitrogen 10 3

M 28, 28 5

c) Oxygen 10 9

M 32, 32 16

d) Argon 10 17

M 36, 36 32





53. One end of a taut string of length 3 m along thex-axis is fixed at x = 0. The speed of the wavesin the string is 100 ms–1. The other end of thestring is vibrating in the y direction so that stationarywaves are set up in the string. The possiblewaveform(s) of these stationary waves is (are) :

a)x 50 t

y(t) Asin cos6 3

b)x 100 t

y(t) Asin cos3 3

c)5 x 250 t

y(t) Asin cos6 3

d)5 x

y(t) Asin cos250 t2

54. The fundamental frequency of a closed organ pipeof length 20 cm is equal to the second overtoneof an organ pipe open at both the ends. The lengthof organ pipe open at both the ends is :

a) 120 cm b) 140 cm

c) 80 cm d) 100 cm

55. A string is stretched between fixed pointsseparated by 75.0 cm. It is observed to haveresonant frequencies of 420 Hz and 315 Hz.There are no other resonant frequencies betweenthese two. The lowest resonant frequency forthis string is :

a) 10.5 Hz b) 105 Hz

c) 155 Hz d) 205 Hz

Brain Teasers

1. A very weakly damped oscillator is acted uponby an external periodic force and is executingsimple harmonic oscillations in a steady state.What is the phase difference between the appliedforce and the oscillator at resonance ?

a) zero b) 4

c) 2

d)

2. A uniform rope 15 m long and of mass 30 kg hangsvertically from a rigid support. A mass of 2 kg isattached at its lower end. A pulse of wavelength1.5 cm is produced at the lower end. What willbe the wavelength at the top ?

a) 2 cm b) 3 cm

c) 4 cm d) 6 cm

3. A vibrating tuning fork is rotated about its stem.What is the maximum and minimum number ofbeats heard by an observer in one revolution ofthe tuning fork ?

a) 1 b) 2

c) 4 d) depends on frequency

4. The equation of stationary wave is,

xy 4sin cos(100 t),

5

where y and x are in metres and t is in seconds.The amplitude of the progressive wave thatproduced the stationary wave is :

a) 1 m b) 2 m

c) 4 m d) 8 m

5. In Q.4, the wavelength of the progressive wavethat produced the stationary wave is :

a) m b) 2 m

c) m5

d) none of the above

6. In Q.4, the velocity of the progressive wave is :

a) 10 ms–1 b) 50 ms–1

c) 100 ms–1 d) 500 ms–1

7. In Q.4, the frequency of the progressive waveis :

a) 10 Hz b) 50 Hz

c) 100 Hz d) 500 Hz





8. In Q.4, the distance between consecutive nodesis :

a) 2 m b) 4 m

c) 5 m d) 10 m

9. Three sources of sound of equal intensities havefrequencies 251, 252 and 253 hertz respectively.When sounded together, the number of beatsheard per second will be :

a) 1 b) 2

c) 3 d) none of the above

10. Two identical organ pipes are producing funda-mental notes of frequencies 200 Hz at 150C. Ifthe temperature of one pipe is raised to 270C, thenumber of beats produced will be :

a) 2 b) 4

c) 6 d) 8

11. The linear density of a vibrating string is 1.3 10–4

kg/m. A transverse wave is propagating on thestring and is described by the equation

y = 0.021 sin (x + 30 t),

where x and y are measured in metres and t inseconds. The tension in the wire is :

a) 0.12 N

b) 0.48 N

c) 1.20 N

d) 4.80 N

12. The end correction of resonance column is 1.0 cm.If the shortest length resonating with a tuning forkis 15.0 cm, the next resonating length is :

a) 31 cm

b) 45 cm

d) 46 cm

d) 47 cm

13. Air is blown at the mouth of a tube (length 25 cmand diameter 3 cm) closed at one end. Velocityof sound is 330 m/s. The sound which is producedwill correspond to the frequencies :

a) 330 Hz

b) Combination of frequencies 330, 660, 990,1320, 1650 Hz

c) Combination of frequencies 330, 990, 1650,2310 Hz

d) Combination of frequencies 300, 900, 1500,2100 Hz

14. A forced oscillator is acted upon by a forceF= F

0sin t. The amplitude of the oscillator is

given by 2

55

2 36 9 . What is the resonant

angular frequency ?

a) 2 b) 9

c) 18 d) 36

15. A wire of length is stretched with a force F andit produces fundamental note of frequency f. Thewave is stretched to double its length and thetension in the wire is kept unchanged. The newfrequency of the fundamental note will be :

a) 2 f b) 2f

c) f d) f

2



DINESH [MHT - CET] PHYSICS


01. (c)

02. (d)

05. (d)

06. (d)

09. (a)

10. (b)

Answer Key

MH Text Book Based MCQ's

01. (b)

02. (c)

03. (c)

04. (b)

05. (d)

06. (d)

07. (b)

08. (c)

09. (c)

10. (a)

11. (c)

12. (a)

13. (c)

14. (b)

15. (b)

16. (c)

17. (b)

18. (a)

19. (b)

20. (a)

21. (a)

22. (c)

23. (c)

24. (d)

25. (c)

26. (c)

27. (d)

28. (c)

29. (d)

30. (b)

31. (d)

32. (c)

33. (b)

34. (b)

35. (b)

36. (b)

37. (d)

38. (c)

39. (c)

40. (c)

41. (c)

42. (a)

43. (a)

44. (a)

45. (d)

46. (c)

47. (c)

48. (a)

49. (a)

50. (d)

51. (a)

52. (b)

53. (d)

54. (a)

55. (d)

56. (d)

57. (b)

58. (b)

59. (d)

60. (d)

61. (c)

62. (d)

63. (c)

64. (b)

65. (c)

66. (d)

67. (b)

68. (c)

69. (b)

70. (c)

71. (c)

72. (d)

73. (c)

74. (c)

75. (b)

76. (d)

77. (c)

78. (c)

79. (a)

80. (b)

81. (b)

82. (d)

83. (a)

84. (b)

85. (c)

86. (b)

87. (c)

88. (c)

89. (b)

90. (a)

91. (a)

92. (c)

93. (d)

94. (a)

95. (c)

96. (b)

97. (a)

98. (b)

99. (c)

100. (d)

101. (c)

102. (a)

103. (a)

104. (b)

105. (b)

106. (c)

107. (c)

108. (c)

109. (d)

110. (b)

111. (c)

112. (a)

REVISION QUESTIONS from Competitive Exams.

01. (b)

02. (c)

03. (c)

04. (b)

05. (d)

06. (c)

07. (a)

08. (b)

09. (b)

10. (b)

11. (a)

12. (c)

13. (b)

14. (b)

15. (b)

16. (d)

17. (c)

18. (b)

19. (b)

20. (a)

21. (b)

22. (a)

23. (b)

24. (d)

25. (c)

26. (b)

27. (a)

28. (b)

29. (a)

30. (d)

31. (b)

32. (c)

33. (a)

34. (d)

35. (b)

36. (c)

37. (b)

38. (c)

39. (d)

40. (c)

41. (b)

42. (c)

43. (b)

44. (b)

45. (c)

46. (b)

47. (c)

48. (b, c)

49. (b)

50. (a)

51. (c)

52. (d)

53. (a,c,d)

54. (a)

55. (b)

BRAIN TEASERS

03. (c)

04. (b)

07. (b)

08. (c)

11. (a)

12. (d)

13. (c)

14. (b)

15. (d)




Hints & Solutions 24

stationary waves

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