A source of sound S of frequency 500 H z situated between a stationary observer O and a wall W, moves towards the wall with a speed of 2 m/s. If the velocity of sound is 332 m/s, then the number of beats per second heard by the observer is (approximately)

Question

A source of sound S of frequency 500 H z situated between a stationary observer O and a wall W, moves towards the wall with a speed of 2 m/s. If the velocity of sound is 332 m/s, then the number of beats per second heard by the observer is (approximately) (A) 8 (B) 6 (C) 4 (D) 2

Tardigrade Admin · Accepted Answer

For direct sound source is moving away from the observes so frequency heard in this case

n_{1} = n (\frac{v}{v + v _{s}})

= 500 (\frac{332}{332 + 2})

= 500 (\frac{332}{334}) Hz

The other sound is echo, reaching the observer from the wall and can be regarded as coming from the image of source formed by reflection at the wall. This image is approaching the observer in the direction of sound.
Hence for reflected sound, frequency heard by the observer is

n_{2} = n (\frac{v}{v - v _{S}})

= 500 (\frac{332}{332 - 2})

= 500 (\frac{332}{330}) Hz

Beats frequency

= n_{2} - n_{1} = 500 \times 332 (\frac{1}{330} - \frac{1}{334})

= 6

Q. A source of sound S of frequency 500Hz situated between a stationary observer O and a wall W, moves towards the wall with a speed of 2m/s. If the velocity of sound is 332m/s, then the number of beats per second heard by the observer is (approximately)

8

6

4

2

Q. A source of sound $S$ of frequency $500 Hz$ situated between a stationary observer $O$ and a wall W, moves towards the wall with a speed of $2 m / s$ . If the velocity of sound is $332 m / s,$ then the number of beats per second heard by the observer is (approximately)