A stationary wave does not have a speed. By reference to the formation of a stationary wave, explain the significance of the product
f
for a stationary wave. [3]
c. Explain what is meant by diffraction of a wave. [2]
d. A narrow beam of coherent light of wavelength 589 nm is incident normally on a diffraction grating having
4.00 10 2
lines for every 1 mm.
i. Determine the number of orders of diffracted light that are visible on each side of the
zero order. [2]
ii. A student suspects that there are in fact two wavelengths of light in the incident beam, one at 589.0 nm and the other at 589.6 nm.
1. State the order of diffracted light at which the two wavelengths are most likely to
be distinguished. [1]
2. The minimum angular separation of the diffracted light for which two wavelengths may be distinguished is 0.10°. By means of suitable calculations, explain whether the student can observe the two wavelengths as separate images. [2]
[Total: 12]
Top view (figure not to scale)
P
Q
runway
anti-nodal lines
13. [RI/H2/Prelims 2010/P3/6]
a. State two conditions for observable interference of two waves. [2]
b. In an aircraft landing system, it is important to guide the aircraft along the centre-line of the runway prior to landing. In a simple landing system, rows of light guides are lined along the runway to help guide the pilot.
The minimum power of light that can be detected by the human eye of area 0.50 cm2 is about 2.5 × 10-11 W. If an aircraft is 12 km away from the runway, find the required power of one light guide such that it is observable by the pilot. Assume that the light guide is a
point source and that there are no energy losses. [3]
c. In another type of landing system, aircrafts are guided using interference of radio waves.
Figure 23 shows two radio wave emitters P and Q positioned 50 m apart at the end of the runway. The two emitters emit radio waves of frequency f1 in phase.
The aircraft can be guided by searching for the strong signal radiated along the lines of constructive interference, also known as anti-nodal lines. To ensure that the aircraft is along the centre-line of the runway, the aircraft needs to “lock on” to the central anti-nodal line.
Figure 23
i. Suggest why radio waves are used instead of waves of shorter wavelengths (e.g.
microwaves, etc.). [2]
ii. Explain why the entire centre-line will always be an anti-nodal line. [2]
d. One particular aircraft at a vertical height of 480 m strays off the centre-line as shown in Figure 24. Figure 25 shows the radio wave signals from P and Q detected by the aircraft in this position.
480 m
P Page 38 of 75
50 m
i. The source of signal B is emitter P. Using Figure 25, explain why this is so. [1]
ii. State the phase difference between signals A and B. [1]
iii. Hence determine the frequency f1 of the radio wave used. [4]
e. As an additional precaution to prevent the aircraft from “locking on” to the wrong anti-nodal line, the emitters can simultaneously emit another radio wave of a different
frequency f2. However, for this precaution to work, the ratio of the two frequencies
1 2
f f
should not be an integer ratio (e.g.
1
i. Explain how this precaution can prevent the aircraft from “locking on” to the wrong
anti-nodal line. [1]
ii. Explain why the ratio of the two frequencies should not be an integer ratio. [2]
f. Suggest one advantage and one disadvantage of the wave-interference system over the light guide system in guiding aircrafts to land safely. [2]
[Total: 20]
14. [RVHS/H2/Prelims 2010/P3/4]
Figure 26 shows a pair of identical loudspeakers A and B placed 2.00 m apart and emitting coherent sound waves of frequency 470 Hz. An observer walks from X to Y. The perpendicular distance between the sources and XY is 12.0 m. As he walks, he hears sound of maximum intensity at P, followed by minimum intensity at Q and the next maximum intensity at R. R is 4.50 m away from P.
(diagram not to scale)
Figure 26
a. Explain why the observer hears sound of maximum and minimum intensity as he moves
from X to Y. [2]
b.
i. AR is 12.5 m, show that BR is 13.2 m to 3 significant figures. [1]
ii. Determine the wavelength of the sound. [2]
iii. Determine the speed of the sound. [2]
c. The power of the loudspeakers A and B are identical. Suggest why the intensity at Q is
not zero. [3]
[Total: 10]
P
X S1
S2
15. [TJC/H2/Prelims 2010/P3/6]
a. What do you understand by interference? [1]
b. Figure 27 shows two loudspeakers S1 and S2 connected to the same sound source such that they emit sound waves of the same intensity and wavelength. A sound detector is placed at point P such that S1P = S2P initially.
Figure 27
i. As the loudspeaker S1 is moved slowly away from P along the line PS1 towards X, the sound detected at P fluctuates in intensity. Explain this observation. [3]
ii. As the loudspeaker S1 is moved towards X through a distance of 0.082 m, the intensity of the sound detected at P decreases from a maximum to a minimum.
Calculate the wavelength of the sound emitted by the sources. [2]
iii. If S1 remains at point X and the frequency f of the sound emitted from both loudspeakers is now gradually changed to 4100 Hz, the sound intensity detected at P increases from the minimum in b.ii. to a maximum. Estimate a value for the speed of
sound. [3]
c. In another experiment to determine the speed of sound, a long tube, fitted with a tap, is filled with water. A tuning fork is sounded above the top of the tube as the water is allowed to run out of the tube, as shown in Figure 28.
A loud sound is first heard when the water level is as shown in Figure 28, and then again when the water level is as shown in Figure 29.
Figure 28 illustrates a stationary wave produced in the tube.
i. Explain the formation of a stationary wave in the tube. [2]
ii. Explain, by reference to resonance, why the loudness of the sound changes as the
water level changes. [3]
iii. On Figure 29, sketch the form of the stationary wave set up in the tube. [1]
iv. The frequency of the fork is 512 Hz and the difference in the height of the water level for the two positions where a loud sound is heard is 32.4 cm.
Calculate the speed of the sound in the tube. [3]
v. The length of the column of air in the tube in Figure 28 is 15.7 cm.
Suggest where the antinode of the stationary wave produced in the tube in Figure 28
is likely
to be found. [2]
[Total: 20]
16. [YJC/H2/Prelims 2010/P3/6 (part)]
White light has a wavelength range from 400 nm to 750 nm. A diffraction grating with 6 × 105 lines per metre is placed at right angles to a ray of white light and produces the first and second order spectra as shown in Figure 30.
First order spectrum Second order spectrum
White light A
Figure 30
a. Show, by calculation, that the angle is greater than . [4]
b. Show, by calculation, whether the second order spectrum overlaps with the third order
spectrum. [3]
c. State two advantages of analysing the light in the first order spectrum. [2]
d. State what would be seen at A. [1]
[Total: 10]
17. [VJC/H2/Prelims 2010/P3/2]
a. The figure below shows a thin taut wire held horizontally by two supports placed 0.40 m apart.
When the wire is plucked at its centre, a standing wave is formed and the wire vibrates in its fundamental mode of frequency 50 Hz.
i. Explain why a standing wave is formed between the supports. [2]
ii. Determine the speed of the wave in the wire. [1]
iii. Sketch the next 2 higher modes which the string can vibrate in and hence determine
their corresponding frequencies. [3]
b. The wire is then connected to an a.c. source in a closed circuit and a magnet is brought near to the wire as shown in the next figure below. This causes the wire to vibrate in its fundamental mode with a large amplitude. When the movable support is shifted from its position, the amplitude of vibration decreases abruptly.
i. Explain the change in amplitude of the wire’s vibration when the movable support is shifted. Hence, deduce the frequency of the a.c. source. [3]
ii. Suggest two ways that the same wire can be made to resonate with a fundamental
frequency of
100 Hz. [2]
[Total: 11]