Q1. What is Doppler's effect in sound waves? Give an example. What is the cause of Doppler's effect?
Solution
When a source of sound is approaching or is being approached by an observer, the pitch of the sound appears to be higher than its normal, and when it is receding or being receded by the observer, the pitch of the sound appears to fall below the normal. This apparent change in the pitch due to the relative motion between the source and the observer (and the medium) is called Doppler's effect.
When a whistling engine approaches an observer who is standing on the platform, he notices a rise in pitch, and fall in pitch when the engine recedes from him.
It can be explained as follows. When the whistling engine is approaching, the engine is following the waves already sent to the observer. This results in crowding up of the waves. The waves reach the observer in quicker succession and the pitch or the frequency, therefore, appears to rise. The converse happens when the engine is receding from the observer.
Q2. (i) A tuning fork T produces n beats/sec with another fork S whose frequency is known to be n1. When T is loaded with wax, the beat frequency decreases. What is the frequency of T?
(ii) On loading T if the beat frequency increases, what will be the frequency of T?
Solution
(i) The frequency of the fork T must be either (n1 + n) Hz or (n1 - n) Hz since n beats are produced initially.
When the fork is loaded with wax, its frequency is reduced.
Hence, if the fork had a frequency (n1 - n) Hz, then the beat frequency would have reduced.
So, the frequency of the unknown fork has to be (n1 + n) Hz.
(ii) Similarly, if the beat frequency increases then the frequency of fork T will be (n1 - n) Hz.
Q3. Name some applications of Doppler's effect.
Solution
(i) We can measure the speed of stars.
(ii) We can measure the speed of aeroplane.
(iii) We can measure the speed of rotation of the sun.
Q4. A set of 28 tuning forks is arranged in a series of decreasing frequencies. The first tuning fork is higher ocatve of last tuning fork. When the two consecutive tuning forks are sound together, 4 beats are produced. Find the frequency of first and last tuning fork.
Solution
Let the frequency of last tuning fork is v. Thus the frequency of first tuning fork will be 2v. As the two successive tuning forks produce 4 beats, therefore the frequency of other tuning fork will be
2v, 2v-4, 2v-8.........................v.
The above series is AP series. For AP series we have
Tn = a + (n-1)d
Here Tn = v, a = 2v,
n = 28, d = -4
Therefore, v = 2v + (28 - 1) (-4)
or v = 108 Hz and 2v = 216 Hz
Q5. If the length of an open end organ pipe is doubled, what changes in its fundamental frequency will occur?
Solution
Fundamental frequency of the open end pipe, n = v/2L.
When the length is doubled,
n' = v/4L = n/2
Thus, the fundamental frequency is halved.
Q6. Write four properties of stationary waves.
Solution
(i) The disturbance is confined to a particular region and there is no onward motion.
(ii) There is no transference of energy in the medium.
(iii) The amplitude of vibration of the particles changes from zero (at nodes) to maximum (at antinodes).
(iv) The particles of the medium at nodes are permanently at rest.
Q7. A large auditorium has a curved back. Why?
Solution
This is done to render the sound waves parallel so that these can be heard over a large distance. The speaker is placed at the focus of curved surface and the sound after reflection from curved surface becomes parallel.
Q8. What is the difference between interference and beats?
Solution
Interference pattern is produced when two waves of same frequency travelling in same direction superimpose, while beats are formed when frequencies are slightly different.
In interference, the position of maximum and minimum are permanent i.e., intensity at a given point does not change with time, but in beats the intensity of wave changes at given point with time.
Q9. Given below are some examples of wave-motion. State in each case if the wave-motion is transverse, longitudinal or a combination of both :
(i) Motion of a kink in a long coil spring produced by displacing the end of the spring sideways.
(ii) Waves produced in a cylinder containing a liquid by moving its piston back and forth.
(iii) Waves produced by a motor boat sailing in water.
(iv) Light waves travelling from the sun to the earth.
(v) Ultrasonic waves in air produced by a vibrating quartz crystal.
Solution
(i) Transverse, because the vibration of particles of the spring are at right angles to the direction of wave propagation.
(ii) Longitudinal, because the molecules of the liquid vibrate to and fro about their mean positions along the direction propagation of the wave.
(iii) Combination of transverse and longitudinal.
(iv) Transverse, because the light waves are electromagnetic waves in which electric and magnetic fields oscillate in the direction at right angles to each other and also to the direction of propagation of the wave.
(v) Longitudinal, because the direction of vibration of air molecules is to and fro about its mean position along the direction of propagation of wave due to the vibration of quartz crystal.
Q10. How does the apparent frequency change when there is relative motion between the source of sound and observer?
Solution
When the source of sound approaches towards stationary observer or observer approaches towards source, the apparent frequency increases and when two recede away from each other the apparent frequency decreases.
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