eu1c2 by adel khamis
TRANSCRIPT
Unit one -68- Chapter Two
Choose the correct answer from those between brackets and write it in your answer paper
Evaluation book:
1. The tension of a string is measured in [kg/m – Newton – m/s – meter](1)
2. The second overtone of a vibrating string is produced when it vibrates in the
form of [one segment – two segments – three segments – four segments](2)
3. When the string vibrates as one segment, its length equals to [2 - - /2 – 3 λ2 ](3)
4. The velocity of propagation of the transverse wave through a vibrating string
is determined from [v= T
√m - v=√T
m - v=√ T
m - v=√ m
T .m ](4)
5. The standing waves are produced due to the superposition of two wave
motions having:(5)
a) The same frequency, amplitude and propagate in the same direction.
b) The same amplitude and propagate in the same direction.
c) The same frequency, amplitude and propagate in the opposite
direction.
d) The same amplitude and propagate in opposite direction.
6. a) A stretched string vibrates as shown in three segments to produce its tone
[fundamental – first harmonic – second
harmonic – third harmonic](6)
b) Using the same figure, the wavelength of the standing wave is [60 cm –
120 cm – 180 cm – 240 cm](7)
Exercises 2008/2009
Unit one -69- Chapter Two
c) Using the given information on the previous figure, the frequency of the
tone produced by the string (the velocity of the transverse wave in the
string 180 m/s) is [600 Hz – 450 Hz – 300 Hz – 150 Hz](8)
d) Using the information given on the previous figure, the frequency of the
fundamental tone of the string is [50 Hz – 100 Hz – 150 Hz – 200 Hz](9)
7. (Egypt 2001) When a string of length (L) vibrates and is divided into (n)
segments, then the wave length of its tone () equals [n/(2L) , L/n, n/L, (2L)/n]
(10)
8. A stretched string vibrates in the form of 5 segments, it emits its ……..
harmonic tone [four – second – third – five](11)
9. A person is standing in a large open field at a distance of 170 m from a vertical
wall, A gun X is sited at a point 34 m from the wall along, the line
perpendicular to the wall and passing through the observer “O” the gun is
fired:
Assuming that the speed of sound in air is 340 m/s what will the observer
hear(12)
a) Two reports only, separated by an interval of 0.2 S
b) Two reports only, separated by an interval of 0.4 S
c) One report only, immediately the gun is fired.
d) One report immediately the gun is fired, followed by a second report
0.25 S later.
Exercises 2008/2009
Unit one -70- Chapter Two
e) It is not possible to say what is heard from the information given.
10. Two stringed instruments are playing notes of the same pitch, which of the
following must be the same for the two notes(13)
a) amplitude
b) frequency
c) length of vibrating string
d) quality
e) tension of the vibrating string
11. When the pitch of a note is raised the(14)
a) Frequency is decreased
b) Speed of the sound is increased
c) Speed of the sound remains the same while wavelength decreased
d) Wavelength remains the same
12. A boy stands at x in open space, between two tall building P and Q, at distance
50 m and 200 m he strikes a drum once
and hears two marked echoes, separated
by a time interval 1 second from these
figure the calculated speed of sound in
air is [150 m/s – 250 m/s – 300 m/s –
330 m/s 500 m/s](15)
Pervious exams:
13. (August 96) The wavelength of a standing wave is [the distance between two
successive nodes, the distance between two successive anti-nodes, twice the
distance between two successive nodes](16)
Exercises 2008/2009
Unit one -71- Chapter Two
14. (August 97) The string emits its second over tone when it vibrates in the form
of [three segments – four segments – five segments](17)
Each question one or more of the responses given is (are) correct. Decide which of the response is (are)
correct, then choose
Evaluation book:
1. The frequency of the fundamental tone produced by a string depends on:(18)
a) Its tension
b) Its length
c) Its mass per unit length
2. The frequency of the string produced first over tone equals:(19)
a) Twice the frequency of its fundamental tone.
b) Three times the frequency of its fundamental tone
c) Five times the frequency of its fundamental tone.
3. The wavelength of the standing wave is:(20)
a) The distance between two successive nodes.
b) The distance between two successive antinodes.
c) Twice the distance between two successive nodes.
4. The ratio between the frequencies of the fundamental tone and that of the over
tones emitted from a vibrating string is:(21)
a) 1: 3: 5
b) 1: 2: 3
c) ¼: ½: ¾
Exercises 2008/2009
Unit one -72- Chapter Two
5. If the string vibrates in the form of two segments:(22)
a) If emits its first harmonic tone
b) If represents the length of a complete standing wave
c) If emits the fundamental tone.
Structured questions
Evaluation book:
1. The given graph represents the relation between
the frequency of the fundamental one of a
stretched string “” and reciprocal its length “1/L”
a) The slope = …………………..(23)
b) The wavelength which emits the string
= ………………(24)
c) The velocity of the wave propagates through the string = slope x
……….(25)
2. A vibrating string emits a tone related to the relation ν= 5
2 L √ Tm where v is
the frequency. L is the length of the string, T is the tension and m is the mass
per unit length.
a) This string emits its ……………….. tone.(26)
b) The wavelength of the propagated wave in the string = ………………(27)
3. If the tension increased 9 times its value and the length of string is increased 3
times, its value then: the frequency of the emitted tone ………… the original
value.(28)
Exercises 2008/2009
Unit one -73- Chapter Two
Previous Exams:
4. (Egypt 2004) When a string vibrates emitting its fundamental tone according
to the relation V=150
L so:
a) The velocity of the transverse wave propagating in the string = ………….
If the length of the string is 50 cm and its mass is 5 gm.
b) The frequency of the fundamental tone emitted by it = ……………..
c) The tension acting on the string = …………
d) The frequency of the third overtone = ……………
Additional Questions:
5. When a string of length 150 cm, and mass 150 gm, vibrates according to the
relation ν ( in hertz )=150
L producing its first over tone, then
a) The frequency of the fundamental tone = ……………
b) The tension of the string = ………………
Essay questions
Evaluation book:
1. (Egypt 94) What are the factors affecting the frequency of fundamental tone of a
vibrating string, mention the relation between each factor and the frequency, and
then write the mathematical relation of these factors with the frequency.(29)
2. Explain Meld’s experiment for the demonstration of standing waves in strings.(30)
3. Write down the relation between the frequency of the fundamental tone and their
overtones in a string.(31)
Previous Exams:
4. (Egypt 99) Mention the necessary condition to obtain a standing wave.(32)
Exercises 2008/2009
Unit one -74- Chapter Two
5. (Egypt 2000) Mention two factors only on which the frequency of the fundamental
tone of a vibrating string depends(33)
6. (August 2000, August 2001) What is the difference between each pair of the
following: The constructive and destructive interference in sound from the point
of view of [the intensity of sound produced and the path difference](34)
7. What happens with mention the reason for each of the following when:
a) (August 2001) Put a balloon filled with helium gas (lighter than air) between
your ear and a source of sound.(35)
b) (Egypt 2002) Increasing the tension on a stretched string to 4 times its value
(with respect to the velocity of propagation of the transverse waves in it)(36)
Give reasons
Evaluation book:
1. The vibrating string produces a tone, whose pitch increases with the tension.(37)
2. As the radius of the stretched string with constant tension decreases the pitch
of the tone increases.(38)
3. The frequency of the fundamental tone is the lowest frequency produced by
the string.(39)
4. We can hear a person talking behind a thick wall.(40)
5. A person under water surface does not hear clearly sound produced from air.
6. The tone produced from a guitar is different than that produced from flute
although they have the same frequency.
Previous exams:
7. (August 97) When the sound transfers from the air to the water, the angle of
refraction is greater than the angle of incidence.
Exercises 2008/2009
Unit one -75- Chapter Two
Additional questions:
8. Astronauts use wireless instruments for their communication on moon’s
surface.
9. A clear sound is heard at the side of the balloon contains CO2 if a sound source
is placed at the other side.
10. Sound refracts away from the normal to the surface as it transfers from air to
water.
Which of the following statements are right and which are wrong? Rewrite the incorrect statements in
a correct form
Previous exams:
1. (Egypt 93) The frequency of the fundamental tone of a vibrating string is
directly proportional to the density of its material.
What is meant by
Previous exams:
1. (Egypt 2002, Egypt 95) The wave length of a standing wave in a stretched string =
10 cm.
Define each of the following physical quantities and write the unit used to measure each of them if
available
Previous exams:
1. (Egypt 90) Standing waves.
Additional question:
2. Interference.
Exercises 2008/2009
Unit one -76- Chapter Two
3. Diffraction.
4. Anti-node.
5. Node.
6. Wavelength of standing wave.
Complete the following statements
Previous exams:
1. (Egypt 96) A vibrating string emits a tone related to the relation ν= 3
2 L √ Tm
where is the frequency, L is the length of the string, T is the tension and m is
the mass per unit length. Complete the following:
This string emits its ………….. tone.
The wavelength of the propagated wave in the string = …………….
If the tension is increased 4 times its value and the length of string is
decreased to the half, then: the frequency of the emitted tone becomes
…………… its original value.
Additional questions:
2. Constructive interference between two waves occurs when the path difference
= …………..(41)
3. The standing waves are produced by …………….. of the incident wave and
the reflected wave, …….. is formed at the middle of the string while ……….
is formed at the ends.
4. The refraction of the sound wave will be clear if the difference in
…………….. between the two media is ….. but if this difference is … so most
of the sound energy ……
Exercises 2008/2009
Unit one -77- Chapter Two
5. The frequency of the stretched string is …. Proportional to its length and
directly to ….. of tension also it is inversely proportional to the square root
of…..
6. The anti node is the position which the amplitude is ……………. while the
node is the position at which the amplitude …..
7. The vibrating string produces its …..tone when it oscillates as one part
forming …..at the middle and …..at its ends.
Problems
Evaluation book:
1. A string 100 cm long produces its fundamental tone of frequency 420 Hz. Find
the length of the string, which produces its fundamental tone of frequency 600
Hz.
[70 cm]
2. A string of length 1m and the mass per unit length of its wire is 0.001 Kg/m
stretched by a tension of 90N. Find
a. The frequency of the fundamental tone produced.
b. The velocity of wave propagating through the string.
c. The frequency of the fourth harmonic.
[150 Hz, 300 m/s, 600 Hz]
3. A stretched string, calculate the velocity of propagation of the transverse wave
in this string known that the tension is 81 N and the mass per unit length is
0.01 kg. If the string is 0.45 m long, calculate the frequency of its fundamental
tone. What is the frequency of its third harmonic?
[90 m/s, 100 Hz, 300 Hz]
Exercises 2008/2009
Unit one -78- Chapter Two
4. A stretched string (T = 128 N, m = 0.02 kg/m) is vibrating in two segments to
produce its first overtone. What is the frequency of this tone if the length of
the string is 40 cm? And what is the frequency of the tone following it?
[200 Hz, 300 Hz]
5. The following table shows the relation between the frequency of the
fundamental tone of a stretched string and the reciprocal of its length when it
vibrates, the tension is kept constant:
1/L “m-1”10A54321
“Hz”50030025
0
B1489846
Draw a graphical relation between the reciprocal of the length on the x-axis
and the fundamental frequency on the y-axis. From the graph find:
a) The values of both A, and B.
b) The velocity of the transverse wave propagating in the string.
c) If the mass per unit length of the string wire is 0.01 kg/m find tension
action on the string.
6. In Meld’s experiment the length of the thread is 2.5 meter, if the wave length
is 0.5 meter, how many nodes and antinodes are formed.
7. A string of mass 2 g and length 1 m is fixed at one end and attached at the
other end to an oscillator of variable frequency. The string is under a tension
of 51 N. find the three lowest oscillator frequencies for which standing waves
will be formed.
Exercises 2008/2009
Unit one -79- Chapter Two
Previous exams:
8. (Azhar 93) A transverse wave propagates in a string of length 2 meters and
mass 0.02 kg in the shape of two parts, tensioned by force of 104 N, calculate
the speed of wave propagation of the wave in the string, and if the wave length
in the air 65 cm, calculate the speed of sound in air.
[1000 m/s, 325 m/s]
9. (Egypt 90) What is occurred in the frequency of a string when its length is
reduced to half and its tension force is reduced to the quarter.
[Remains constant]
10. (Egypt 95) An elastic string 2 meter long producing its fundamental tone of
frequency 400 Hz if the wave length of the produced wave in air is 80 cm.
calculate:
a. The velocity of sound wave in air.
b. The velocity of wave in the string.
[320 m/s, 1600 m/s]
11. (August 96) A string of length 1 m is stretched by a force of 4 kg wt. the mass
per unit length is 1 x 10-3 kg/m. what is the frequency of its fundamental tone
and its first overtone (g=10 m/s2)
[100 Hz, 200 Hz]
12. (Egypt 98) The following table shows the relation between the inverse of the
length of a uniform string and the frequency of its fundamental tone when it
vibrates. The tension is kept constant.
(1/L) m-11X23456
() Hz150210300450600Y900
Exercises 2008/2009
Unit one -80- Chapter Two
Draw a graphical relation between the reciprocal of the length on the x-axis,
and the fundamental frequency on the y-axis. From the graph find:
a. The frequency (y).
b. The length of the string that emits its fundamental tone with frequency
(210) Hz.
c. The velocity of the transverse wave propagating in the string.
d. If the mass per unit length of the string wire is 0.01 kg/m, find the tension
acting on the string.
[750, 1.4. 300, 900]
13. (Egypt 2006) A string from steel of length 1 meter vibrates in the form of
segments, it produces a frequency of 150 Hz, if the mass per unit length of the
string is 0.01 Kgm-1 the string is stretched by tension force 10 kg wt, what are
the number of segments in which the string is divided during its vibration,
given that g = 10 m/s2, calculate the velocity of the propagation and draw the
formation of produced tone.
[3, 100m/s]
Additional questions:
14. A gun is fired; a person heard the sound of the bullet after 20 seconds from
seeing the fire. If the distance between the person and the gun is 6800 meters
calculate the sound velocity.
[340 m/s]
15. Find the velocity of a transverse wave propagates in a stretched string such
that tension is 10 kg weight; the mass per unit length is 0.02 kg/m. given that
the acceleration due to gravity is 9.8 m/s2.
[70 m/sec]
Exercises 2008/2009
Unit one -81- Chapter Two
16. Find the frequency of the third harmonic tone of a string stretched by tension
10 kg weight and the mass per unit length is 0.02 kg/m and the acceleration
due to gravity is 9.8 m/s2. Given that the length is 0.5 m.
[210 Hz]
17. A string of length 0.5 meter is stretched by a tension of 28.9 Newton. The
mass per unit length of the string equals 0.001 kg/meter. If the velocity of
sound in air is 340 meter / sec, calculate:
a) The frequency of the fundamental tone produced by the string.
b) The wavelength in air.
[170 Hz, 2 m]
18. A string 1 meter long and the mass of its wire is 0.0001 kg stretched by a
tension of 81 N. Find:
a) The frequency of the fundamental tone it produces.
b) The velocity of the wave propagating through the string.
c) The frequency of the third overtone.
[450 Hz, 900 m/s, 1800 Hz]
19. The following table gives the relation between frequency of fundamental tone
of vibrating string and its length:
L (m)0.10.20.250.40.50.60.8X
V(Hz)500250200125100y62.550
a. Plot a graph relation between L and v and deduce the relation between
them.
b. Find the velocity of transverse wave in string.
c. Find the value of x and y.
Exercises 2008/2009
Unit one -82- Chapter Two
20. A person stands up between two mountains and he is nearer to one of them
than the other mountain, he shoots a project, he heard two sounds: the first one
after 1.5 sec, and the second after 3 sec. Calculate: the distance between the
two mountain, given that the speed of sound in air is 320 m/s
[450 Hz, 900 m/s, 1800 Hz]
21. A ship is moving towards a mountain on seashore with regular velocity, when
it was (1 km) far from the mountain the ship makes a whistle, the echo was
heard after (5 sec), if the velocity of wound in air (340 m/s) calculate the
velocity of the ship.
[60 m/s]
22. A stretched string (60 cm) long vibrates at frequency of (100 Hz), at what
frequency would it vibrate if its length was reduced to (15 cm) but the tension
was unaltered.
[400 Hz]
23. A string of length (1.5 m) vibrates in the form of (6 segments), its mass =
(0.15 kg) tensioned by a force of 10 N, find the frequency of sound that the
string emits.
[20 Hz]
24. Two strings (A), (B) are from the same material and equal in length, knowing
that the diameter of (A) is half that of (B) and is stretched by a tension force
(20 N) calculate the tension force of (B) to produce the same fundamental tone
of (A)
[80 N]
25. A stretched string of length (L) produce fundamental tone of frequency (120
Hz), Calculate the frequency of this string when:
Exercises 2008/2009
Unit one -83- Chapter Two
a) The length decreases to its half value.
b) The tension increases to four times its original value.
[240 Hz, 240 Hz]
26. A string is stretched by a force of 100 N, its length is 2 m, its mass is 0.02 kg,
(g = 10 m/sec) Calculate:
a) The speed of propagation of the wave in it.
b) The frequency of the fundamental tone.
[100 m/s, 25 Hz]
27. A string is stretched on a sonometer, its frequency (500 Hz) when its tension
was 36 N, calculate the frequency of the string when the tension becomes (25
N).
[416.67 Hz]
28. String of length equal (80 cm) and its unit length has mass equals 0.4 gm, it is
stretched by a tension equals 49 N, calculate the frequency of the string tone,
if it vibrates at the shape of four parts.
[875 Hz]
29. Two strings have a length 80 cm and 100 cm respectively and radii (2 mm, 3
mm) respectively and the frequency of the second string is 160 Hz, calculate
the frequency of the first string given that the tensions are equal.
[300 Hz]
30. Two strings have the same material, the length of the first string is double the
length of the second, the radius of the second string is double the radius of the
first, compare between the frequency of both strings when the tension force
are equal.
Exercises 2008/2009
Unit one -84- Chapter Two
[equal]
31. A string has a length (50 cm), and its radius (0.5 mm), it is stretched by a force
of 12.1 kg.wt, its density equals 7700 kg/m3. Calculate the frequency of the
fundamental tone of the string.
[140 Hz]
32. Length of a string (54 cm) and its mass (10.8 grams), it is stretched over a
guitar by a force (10 kg. wt) calculate the point of string in which a musician
press by his finger on to produce the second over tone with frequency 210 Hz.
[4 cm]
33. A stretched string emits (500 Hz), and when its length is double it emits (750
Hz). Calculate the ratio between the two tensions.
[1: 9]
34. A string of length 150 cm, and mass 1.5 gram, and tensioned by force of 90 N,
calculate the frequency of fundamental tone, the speed of waves in the string,
the frequency of the second over tone.
[100 Hz, 300 m/s, 200 Hz]
35. The length of a string is 2 meter, produces a fundamental tone its frequency
400 Hz, and the length of the produced wave 80 cm, calculate :
a) The speed of sound in the air
b) The speed of wave propagation in the string
[320, 1600 m/s]
36. The length of a string is one meter and its mass (40 gm), stretched with a force
of 196 N, calculate the frequency of the fundamental tone given that
Exercises 2008/2009
Unit one -85- Chapter Two
gravitational acceleration 9.8 m/s2 then deduce how to increase the value of
frequency to 70 Hz, through:
a) Change the length only.
b) Change the tension only.
[35.5 cm, 784 N]
37. A string of mass 2.5 kg is under tension of 200 N, the length of the stretched
string is 20 m, if a transverse vibration begins at one end of the string, how
long does the vibration take to reach the other end.
[0.5 s]
38. A steel wire has a length of 12 m and mass of 2.1 kg, what should be the
tension in the wire so that the speed of a transverse wave on the wire equals
343 m/s
[2.06x104 N]
39. In meld's experiment used a vibrator of fixed frequency, when a load of
volume (V) and density 2700 kg/m3 was hanged at the end of the thread, the
thread divided into 6 segments, when another load of the same volume and of
different material the number of segments becomes 4 segments, calculate the
density of the other load.
[6075 kg/m3]
40. A wire stretched between two rigid supports vibrates in its fundamental tone
with frequency of 45 Hz, the mass of the wire is 3.5 x 10-2 kg, and its linear
density is 4x10-2 Kg/m, what is the speed of its transverse waves.
[78.75 m/s]
Exercises 2008/2009
Unit one -86- Chapter Two
41. The speed of a wave on string is 160 m/s when the tension force in the string is
100 N, to increase the speed to 200 m/s to what value must the tension must
increase.
[156.25 N]
42. If the tension force acting on a string stretched on a sonometer is changed
from 6.4 N to 8.1 N, knowing that it produce its fundamental tone in each
case, find the ratio between the two frequencies keeping its length constant.
[8: 9]
Exercises 2008/2009
Unit one -87- Chapter Two
Model Answers
Exercises 2008/2009
1 () Newton.
2 () Three segments
3 () /2
4 () v=√ T
m
5 () C
6 () Third harmonic
7 () 120 cm
8 () 150 Hz
9 () 50 Hz
10 () (2L)/n
11 () five
12 () a
13 () b
14 () c
15 () 300 m/s
16 () twice the distance between two successive nodes
17 () three segments
18 () a, b, c
19 () a
20 () c
21 () b, c
22 () b
23 () 1/2 velocity
24 () 2 L
25 () 2
26 () Fifth harmonic tone (fourth over tone)
27 () 2L/5
28 () Equal to
29 () Length of the string: υ∝ 1
L
Tension force: υ∝√F t
Mass per unit length: υ∝ 1
√m
υ= n2L √ Ft
m
30() Melde’s experiment:
1. The apparatus is consists of a vibrating source, connected to a soft string whose length
ranges from 2 to 3 meters.
2. The other end of the string passes over a smooth pulley and is connected at its free end to
appropriate weights.
3. When the source vibrates, a wave train is produced in the string, which reflects upon
reaching the pulley.
4. The reflected and incident waves are combined to form standing waves.
31() 1: 2: 3
32() Two waves in phase but opposite in direction.
33() Length of the string, tension force and mass per unit length of the string.
34()
Item Constructive Distractive
Intensity of sound High Low
Path difference m (m+1/2)
35() Fade of sound due to diffraction of sound when it travel from high density (low velocity) to less
density (high velocity).
36() Velocity double where velocity is directly proportional to the square root of tension force.
37() Because the pitch (frequency) is directly proportional to the square root of tension force.
38() Mass per unit length is directly proportional to the reduce of the string, then decrease the reduce
will decrease the mass per unit length. The frequency is inversely proportional to square root of
mass per unit length, then increase the mass per unit length leads to decrease the frequency.
39() Because it has the smallest number of segments and frequency is directly proportional to the
number of segments.
40() Duce to diffraction beside sharp edge.
41 () The path difference between two waves = m