Question

A car moves with a speed of 54 km/h towards a cliff. The horn of the car emits a sound of frequency 400 Hz at a speed of 335 m/s. (a) Find the wavelength of the sound emitted by the horn in front of the car. (b) Find the wavelength of the wave reflected from the cliff. (c) What frequency does a person sitting in the car hear for the reflected sound wave? (d) How many beats does he hear in 10 seconds between the sound coming directly from the horn and that coming after the reflection? 

Answer 1

The frequency of the sound = 400 Hz The speed of sound in air V = 335 m/s 

The speed of car u = 54 km/h = 54000/3600 m/s =15 m/s 

 (a) The apparent frequency in front of the car v' = Vv/(V-u) =335*400/(335-15) Hz =418.75 Hz 

Hence the wavelength = V/v' = 335/418.75 m = 0.80 m 

= 80 cm  

(b) The same apparent frequency will be reflected by the cliff, hence the wavelength of the reflected frequency will be the same i.e. 

= 80 cm  

(c) For the person sitting in the car, the apparent frequency reflected by the cliff is the frequency from the stationary source while the observer is moving at a speed of 15 m/s. Hence the frequency heard by him = (V+u)v'/V 

= (335+15)418.75/335 Hz 

= 350*418.75/335 Hz 

≈ 437 Hz  

(d) The beat frequency reached the person in the car  

= 437 -400 Hz 

= 37 Hz 

Since the beat frequency is more than 16 Hz which is beyond the normal person's perception, hence the person may not hear any beat.