1. A plane water wave reaches an obstacle and passes through the gap of the obstacle. Which one of the following diagrams shows the most probable resultant wave after passing through the gap? (The lines denote the crest of the water wave.)

ACJC 08P1Q23 ________________________________________________________________________________________________________

2. Two monochromatic radiations X and Y of wavelengths λx and λy respectively, are incident normally on a diffraction

grating. The second order intensity maximum for X coincides with the third order intensity maximum for Y. What is the ratio of λx/ λy ? A 1/2 B 2/3 C 3/2 D 2/1

AJC 08P1Q21

________________________________________________________________________________________________________ 3. If two waves of the same frequency are superposed in phase, the total intensity is proportional to

A the square of the sum of the two amplitudes. B the square of the mean value of the two amplitudes. C the square of the difference of the two amplitudes. D the sum of the intensities of the waves.

AJC 08P1Q23

________________________________________________________________________________________________________

4. (a) What is meant by the term superposition when applied to waves? [1] (b) Two loudspeakers L1 and L2 driven from a common oscillator are arranged as shown in Fig. 3.1. A detector is

placed at D. It is found that, as the frequency of the oscillator is gradually changed from 200 Hz to 1000 Hz, the detected signal passes through a series of maxima and minima.

(i) Explain how the maxima and the minima can be observed at the same point D. [2] (ii) Calculate the frequency at which the first minimum is observed. Assume the speed of sound is 340 ms

-1.

[2]

(iii) It is found that when the detector is placed at the central point O, maximum called zero order maximum is always observed for all frequencies of the oscillator. Explain. [1]

(iv) If the frequency of the oscillator is fixed at 510Hz, how far from D must the detector be placed in order to

observe the first order maximum? [2]

AJC 08P2Q3 ________________________________________________________________________________________________________

5. The principle of superposition applies only if A the waves travel with the same speed. B the sources of the waves are coherent. C the waves have the same frequency. D the waves are of the same kind.

CJC 08P1Q20

________________________________________________________________________________________________________

6. S1 and S2 are two identical, small loud-speakers 0.50 m apart and connected to the same audio frequency generator. They vibrate in phase producing sound waves of wavelength 0.40 m

A microphone detects a minimum in the pattern of superposition at the point P. If P is 12.00 m from S2 and PS1 > PS2 then the least possible distance of P from S1 is

A 12.15 m B 12.20 m C 12.40 m D 12.50 m

CJC 08P1Q21

________________________________________________________________________________________________________ 7. Monochromatic light of wavelength 600 nm is incident normally on a diffraction grating having 2 × 105 lines per metre.

What is the angle between the highest order diffracted beam and the normal? A 46˚ B 57˚ C 74˚ D 90˚

CJC 08P1Q23

________________________________________________________________________________________________________ 8. Two small loud speakers A and B are positioned 1.5 m apart in a large room and are connected to the same signal

generator. The loud speaker emits a note of frequency 3400 Hz. A microphone connected to an oscilloscope is placed at P which is equidistant from the two speakers as shown in the figure 3.1. Figure 3.2 shows the trace on the oscilloscope.

The speed of sound in air at room temperature = 340 m s-1

.

(a) (i) What adjustments should you make to the oscilloscope to obtain the trace as shown in figure 3.2 ? [1] (ii) State clearly what the trace height represents. [1]

(b) As the microphone is moved along the line XY, the trace height passes through a series of maxima and minima,

with a maximum at P.

(i) Explain the variation in trace height as the microscope is moved along XY. [2] (ii) Calculate the approximate distance from P to Q, the position of the first minimum. Explain why your

calculation is only an approximation.

(c) The frequency of the signal generator is increased gradually. Suggest and explain qualitatively what an observer would hear if he stays at Q without moving.

CJC 08P2Q3

________________________________________________________________________________________________________ 9. In the Young’s double slit arrangement shown below, a pattern of equally spaced parallel interference fringes appears on

the screen. The slit width is a while the separation between the slits is d. The distance from the screen to the slits is unchanged.

Which one of the following changes would cause the separation of interference fringes to be doubled? A Slit width is a/2 B Slit width is 2a C Slit separation is d/2 D Slit separation is 2d

IJC 08P1Q22

________________________________________________________________________________________________________ 10. A certain diffraction grating has 400 lines per mm. A beam of continuous spectrum white light was projected onto it. How

many orders of the entire visible spectrum (400 nm – 700 nm) can it produce, excluding the zeroth order?

A 3 B 4 C 6 D 8

IJC 08P1Q23

________________________________________________________________________________________________________ 11. (a) (i) Define diffraction. [1]

(ii) Given an explanation for each of the following:

1. One can hear around corners, but not see around corners. [1]

2. Two flashlights held close together do not produce observable interference pattern on a distant

screen. [1]

(iii) Describe the changes to the peak intensity and width of the central maximum of the single-slit diffraction

pattern when the width of the slit is made narrower. [2]

(b) (i) Coherent light rays of wavelength l strike a pair of silts separated by distance d at angle of θ1 as shown

in Fig. 6.1 below. Assume an interference maximum is formed at an angle θ2 and the screen is at a great distance from the slits.

Derive the condition for constructive interference in this case in terms of d, θ1, θ2 , λ and n where n is an

integer. [2]

(ii) Fig.7.2 shows a radio-wave transmitter and a receiver separated by a distance 3000 m apart and both

has a height 80 m above the ground. The receiver can receive signals both directly from the transmitter and indirectly from signals that reflect from the ground. Assume that the ground is level and a 180° phase shift occurs upon reflection.

Determine the longest wavelengths that interfere 1. constructively and [2] 2. destructively. [2]

(c) (i) In a Young’s experiment, two narrow and parallel slits separated by 0.250 mm are illuminated by green

light (l = 546.1 nm). The interference pattern is observed on a screen 1.20 m away from the plane of the slits.

Determine the distance 1. between the first order maxima on either sides of the central maximum [2] 2. between the first order maximum on one side and the second order minimum on the other side

of the principal axis. [2]

(ii) It is possible to observe the interference effect in (c)(i) using electrons which are particles. Explain the

necessary modifications required for the experimental set-up. [3]

(iii) Describe the changes to the fringe pattern observed in (c)(i) if the number of parallel slits is increased.

[2]

IJC 08P3Q6 ________________________________________________________________________________________________________

12. (a) Water waves of wavelength 4.0 m are produced by two generators, P and Q as shown in Fig. 8.1 (Not to scale).

Each generator, when operated on its own, produces waves with amplitude of 20 mm at point R such that PR and PQ are perpendicular to each other. The frequency of the motor of both generators is 2.0 Hz and the generators are operating in anti-phase. Assume the speed of water waves remain unchanged.

(i) 1. Show that the length of QR is 26 m. [1]

2. Determine the path difference between the two water waves arriving at point R from P and Q in terms of the number of wavelengths. [2]

3. Hence, state if constructive or destructive interference takes place at point R and the resultant amplitude of the water wave at point R. [1]

(ii) 1. The frequency of the motor of both generators is now increased to 2.25 Hz. Calculate the new

wavelength of the water waves. [1] 2. Determine the corresponding path difference between the two water waves arriving at point R

from P and Q in terms of the number of wavelengths. [1] 3. Hence, state if constructive of destructive interference now takes place at point R and the

corresponding resultant amplitude of the water wave at point R. [1]

(b) The following short passage is based on extracts from the catalogues of suppliers of college scientific equipment. Read the passage and answer the questions that follow.

HELIUM-NEON LASER AND ACCESSORY SET

This laser emits an intense, coherent monochromatic light of wavelength 650 nm and power output 1.0 mW. The beam is plane-polarised. Also available is a range of slits and gratings to illustrate the phenomena of interference and diffraction.

(i) Define the following terms found in the passage:

1. Coherent [1] 2. Monochromatic [1] 3. Interference [1] 4. Diffraction [1]

(ii) Describe briefly how you would confirm that the laser beam is plane-polarised. [2] (iii) The laser beam is used as a light source for a set up for performing an optical double slit interference

experiment as shown in Fig 8.2.

1. Is the interference pattern on the screen visible?

If so, state a possible colour of the maximas. [1] 2. Calculate the distance between adjacent maximas. [2] 3. The same setup was used again, but the double slit is replaced with a diffraction grating of 350

lines per millimeter. What is the maximum number of maxima? [2]

4. The wavelength of the laser light can be calculated using the setup. Suggest one advantage and one disadvantage of obtaining the wavelength by using observations of the third-order diffracted light rather than the first order diffracted light. [2]

JJC 08P3Q8

________________________________________________________________________________________________________ 13. A parallel beam of white light is incident normally on a diffraction grating. It is noted that the second-order and third-order

spectra partially overlap. Which wavelength in the third-order spectrum appears at the same angle as the wavelength of 600 nm in the second-order spectrum?

A 300 nm B 400 nm C 600 nm D 900 nm

MI 08P1Q22 ________________________________________________________________________________________________________

14. (a) Two coherent sound sources are set up at A and B as shown in Fig. 3.1. A and B are 2.00 m apart. A listener

walks from X to Y. The perpendicular distance between the sources and XY is 12.0 m. As he walks along, he hears sound of maximum intensity at P. The next position of maximum intensity is at Q. The distance between P and Q is 4.00 m.

Fig. 3.1

(i) Calculate the path difference between the waves arriving from A and B at Q. [2]

(ii) Find the wavelength of the sound produced by the speakers. [1] (iii) Given that the frequency of the sound emitted is 520 Hz, calculate the speed of sound in air. [1]

(b) A student sets up the apparatus as shown in Fig. 3.2 to investigate longitudinal stationary waves in an open-end pipe

with a movable slider for adjustment of length.

(i) Explain why it is necessary to adjust either the length of the pipe or the frequency of the sound in order to obtain a stationary wave in the pipe. [2]

(ii) Given that the length of the pipe is 1.5 m, find the frequency of the sound in order to obtain the note with the lowest frequency. You may assume speed of sound in air to be 330 m s-1. [2]

(iii) What is the frequency of the lowest note that is heard when one of the ends is now closed? [2] (iv) With both its ends open, the length of the pipe is adjusted until the next higher note is heard.

In Fig. 3.2, sketch how the amplitude of the stationary wave will vary along the pipe for this new

resonant frequency. [1]

MI 08P3Q3 ________________________________________________________________________________________________________

15. S1 and S2 are two identical sources of waves that are in phase. The instantaneous positions of two wave crests from each

source are shown below. Which of the following is true?

A X is a point of constructive interference. B W is a point of destructive interference. C S1Z – S2Z = (2n - 1) λ/2 where n is an integer. D S1Y – S2Y = n λ where n is an integer.

MJ 08P1Q19 ________________________________________________________________________________________________________

16. Figure 22 shows, to scale, 2 coherent EM sources S1 and S2 which are initially 4π radians out of phase. The wavelength

of the EM wave is 476 μm. When a detector is moved from O to P along the line OP, how many maxima are detected, inclusive of that at O if any?

A 1 B 2 C 3 D 4

NJ 08P1Q22

________________________________________________________________________________________________________ 17. Figure 23 shows the first diffraction order obtained on each side of the zeroth order when a beam of monochromatic light

is incident on a diffraction grating of slit separation d.

Which of the following 1st two orders of the pattern shown, on the same scale is obtained when the grating is changed to one with slit separation d/2?

NJ 08P1Q23 ________________________________________________________________________________________________________

18. (a) The diagram shows a cross-section through a compact disc (CD). The metal layer of a CD is the recording

surface and contains narrow ridges, which form a spiral around the disc.

Red monochromatic laser light of wavelength 780 nm is used to view these ridges. When the light meets a ridge some of it scatters in all directions and some interferes destructively with light reflected from neighbouring valleys. When this occurs, the player is able to read the information from the disc.

(i) Explain the meaning of the term “monochromatic”. [1] (ii) If the ratio of the speed of the laser light in air to the speed of the laser light in the polycarbonate plastic

is 1.55, show that the wavelength of the laser light in the polycarbonate plastic is approximately 500 nm. [2]

(iii) The height of the ridges on a CD is approximately 125 nm. Use your answer in (a)(ii) to explain how

destructive interference occurs. [2] (iv) The infrared laser standard was fixed in 1980 because of the reliability and availability of relatively

inexpensive lasers, which emit at 780 nm. However, blue light lasers are now being developed and the technology called Blu-Ray is fast emerging. These blue light lasers have a wavelength about one half of the red light lasers. Will it be possible to play existing CDs using a Blu-Ray player? Explain your answer. [2]

(v) Music from a CD is played with the speaker placed near the open end of a tube which is closed at the far end. As the CD is played, it was observed that at some instances the music was much louder near the open end of the tube. Explain. [3]

(b) (i) Explain the phenomenon of diffraction, stating an important condition for significant diffraction to occur.

[2] (ii) A diffraction grating with 300 lines per millimeter is being used in a typical light experiment. Different

types of light are allowed to fall normally on a diffraction grating and the resultant pattern formed is to be studied. The first light source to be studied is a white light consisting of wavelengths between 400 nm and 700 nm.

1. Find the maximum order of the complete spectrum that can be observed. [2] 2. Find the order of the pure spectrum before the first overlapping between two higher order

spectra. [3]

(iii) The next experiment is of light from a low pressure sodium lamp. Light from the lamp consists mostly of two wavelengths, 588.99 nm and 589.59 nm.

1. State and explain quantitatively the problem that would likely arise in observing the spectral

lines? [2] 2. Suggest a refinement to the set up to help overcome this problem. [1]

NJ 08P3Q5

________________________________________________________________________________________________________ 19. Two waves of the same frequency are superposed at a point in phase. Huang Lin will observe that the total intensity at

that point is proportional to

A the sum of the intensities of the two waves. B the square of the sum of the two amplitudes. C the square of the mean value of the two amplitudes. D the square of the difference of the two amplitudes

DHS 08P1Q20 ________________________________________________________________________________________________________

20. Waves from a radio station have a wavelength 300 m. They arrive at Kerina’s receiver 20 km away from the transmitter by

two paths. One is a direct path, and the second is by reflection from a mountain directly behind Kerina’s receiver as shown below. What is the minimum distance, in m, from the mountain to Kerina’s receiver such that destructive interference occurs at the receiver?

A 600 B 300 C 200 D 75

DHS 08P1Q21

________________________________________________________________________________________________________ 21. White light covers the range of wavelength 400 nm to 700 nm. Li Hui placed a diffraction grating with 6.0 x 105 lines per

metre at right angles to a ray of white light and produces the first and second order spectra as shown, which is not drawn to scale.

The angle between the red and blue ends of the spectrum is α for the first order spectrum and β for the second order spectrum. How do α and β compare?

A B C D

DHS 08P1Q22

________________________________________________________________________________________________________ 22. An experiment was carried out to determine the wavelength of

monochromatic light using a diffraction grating which has N lines per unit length. A diffraction angle θ for each order m was determined. The graph shows the variation of sin θ with m.

What is the wavelength of the light?

A Nb

a B

Na

b C

b

Na D

a

Nb

NYJ 08P1Q19

________________________________________________________________________________________________________ 23. When a beam of laser is shown on to a vertical slit as shown in Fig. 1, we can see a spot of light on the screen as expected.

As the slit is made narrower and narrower, the spot of light becomes wider and wider in the X direction.

(a) By considering the laser beam as an electromagnetic wave, explain the phenomenon using wave theory. [1] (b) By considering the laser beam as consisting of a stream of photons, use Heisenberg Uncertainty Principle to explain

this phenomenon. [2] (c) A laser beam of wavelength 635 nm is used in the above experiment. Find the momentum of a photon in this laser

beam. [2]

(d) If the width of the slit is 2.0 x 10-5

m, and the uncertainty x of the position of a photon passing through the slit is

approximately of the same value, calculate the uncertainty of the momentum px of the photon using the following

Heisenberg uncertainty equation: x

x p h . [2]

(e) Find sin using the results from (c) and (d). [1]

(f) In wave theory, the angle of such single slit diffraction experiment is given by

sin where a is the width of the slit

and is the wavelenght of the light.

a

Calculate the angle using this equation. [1]

(g) Comment on your answers obtained in (e) and (f). [1]

NYJ 08P3Q4 ________________________________________________________________________________________________________

24. (a) Explain what is meant by superposition in the context of waves. [2]

(b) Two microwave sources S1 and S2 are situated as shown below. The waves emitted by the two sources are in phase and are polarized in the same plane.

px

p

Top view

Image when slit is wide

Image when slit is made

narrower and narrower

X

Y

A microwave detector is placed on a line XY which is parallel to and 3.2 m from the line joining S1 and S2. O lies on the perpendicular bisector of the line joining S1 and S2. The detector produces an output which is proportional to the displacement of the wave detected.

The detector is placed at P, a distance of 5.0 cm from O. The variation of the output of the detector with time with (a) only S1 switched on and (b) only S2 switched on are shown below.

(i) Using the figure above, determine the phase difference between the waves at P. [1] (ii) Calculate the wavelength of the microwaves. [3]

(iii) The sources S1 and S2 are switched on together and as the detector is moved from P towards X, the intensity

of the microwave detected fluctuates.

Assuming there are no maxima between O and P, deduce the distance from O to a point Q where the detector firsts encounters a maximum. [2]

(iv) The graph below shows how the intensity of the detected radiation varies between O and Q when only S1 is switched on.

O

P

5.0 cm

X

Y

3.2 m

S1

S2

0.5 1.0 1.5 2.0

det

ecto

r o

utp

ut

t / 10-10 s

S2 only

S1 only

Using the same axes, sketch a graph to show how the intensity of the detected microwave between O and Q

varies when both S1 and S2 are switched on. Label this graph (iv). [2] (v) Using the same axes as in (iv), sketch a graph to show how the intensity of the detected microwave between O and Q varies if the waves from the sources are polarized in perpendicular planes. Label this graph (v). Explain briefly your answer. [2] (vi) Find the ratio of I1 / I2, where I1 is the intensity of the microwaves detected at Q when S1 and S2 are polarized 2 is that when S1 and S2 are polarized in perpendicular planes. [3] (c) Microwaves such as those in (b) exert pressure on its detector. (i) Explain why this is so. [3] (ii) Deduce and explain the quantitative relationship between the amplitude of a microwave and the pressure it exerts. [2]

NYJ 08P3Q6 ________________________________________________________________________________________________________

25. A diffraction grating with 400 lines per mm is illuminated with yellow light of 600 nm. What is the angle the second maxima

makes with the principal axis? A 2.75˚ B 13.9˚ C 28.7˚ D 73.7˚

PJ 08P1Q19

________________________________________________________________________________________________________ 26. The diagram shows a Young’s Double Slits experiment and the light source from S1 and S2 are assumed to be equal

amplitude. M is at the centre of the zeroth order bright fringe. The light intensity at M for the zeroth order fringe is 2I.

Which of the following is the best estimate for the light intensity at M when S2 is covered? A 0.5 I B 1 I C 2 I D 4 I

PJ 08P1Q20 ________________________________________________________________________________________________________

27. Fig. 5.1 shows two coherent loudspeakers S1 and S2 placed 4.0 m apart in an open field on a calm day. D is a detector

placed in the same horizontal plane as the loudspeakers. D is placed 12.0 m away from S2. When the loudspeakers are switched on, sound of frequency 1780 Hz is emitted from the two loudspeakers in antiphase. The lines S1S2 and S2D are perpendicular to each other.

O Q

S1 only

Intensity / 10-3 W m-2

1.0

(a) Given that the speed of sound in air is 330 ms

-1, calculate the wavelength λ of the sound emitted from S1 and S2.

[1] (b) Calculate the path difference, in terms of λ, between the sound waves reaching D from S1 and S2. You may

assume that the two loudspeakers and the detector are point objects. [2] (c) Using your answer in part (b), state the phase difference between the sound waves reaching D from S1 and S2.

Hence, explain whether D would detect a minimum or maximum intensity. [3] (d) As the frequency of the sound from S1 and S2 is gradually increased from 1780 Hz to a value fnew, D detects 2

complete cycles of change in sound intensity. Calculate fnew, the frequency at which the second complete cycle of change in sound intensity is detected. [3]

PJ 08P2Q5 ________________________________________________________________________________________________________

28. Plane waves of wavelength λ in a ripple tank approach a straight barrier parallel to the wave crests. There is a gap of

width w in the middle of the barrier. Which of the following λ and w will produce the largest diffraction? λ / cm w / cm

A 0.5 2.0 B 0.5 4.0 C 1.5 2.0 D 1.5 4.0

RJ 08P1Q21 ________________________________________________________________________________________________________

28. White light covers the range of wavelength from 400 nm to 700 nm. A diffraction grating with lines per metre is

placed perpendicular to a ray of white light and produces the first order spectrum as shown in the diagram, which is not drawn to scale.

What is the angle θ between the red and blue ends of the spectrum? A 8.6° B 9.0° C 11.5° D 20.5°

RJ 08P1Q22

________________________________________________________________________________________________________ 29. Fringes of separation y are observed in a plane 1.00 m from a Young’s double-slit arrangement illuminated by yellow light

of wavelength 600 nm. At what distance from the slits would fringes of the same separation y be observed when using blue light of wavelength 400 nm?

A 0.33 m B 0.67 m C 0.75 m D 1.50 m

SAJ 08P1Q20

________________________________________________________________________________________________________ 30. Monochromatic light of wavelength 6 × 10−7 m is incident normally on a plane diffraction grating with 5 × 105 lines per

metre. The total number of directions in which a bright line is produced is

A 3 B 5 C 7 D 9

SAJ 08P1Q22 ________________________________________________________________________________________________________