A sound source vibrates at 200 Hz and is receding from a stationary observer at 18 ms⁻¹. If the speed of sound is 331 ms⁻¹ then what frequency does the observer hear? (189.68Hz) 



Given:

Frequency of the source = f = 200 Hz
Speed of the sound of the source = `\v_s` = 18 m s⁻¹
Speed of the sound = v = 331 m s⁻¹

To Find:

The frequency observed by the observer (apparent frequency)  = f' = ?

Solution:

As the source is moving away (receding) from the stationary observer so the apparent frequency f' is given by 


f' = `\frac {v}{v + v_s}` f


f' = `\frac {331 m s⁻¹}{331 m s⁻¹ + 18 m s⁻¹}` ｘ 200 Hz

by simplifying 

f' = 189.685 Hz

or

f' = 190 Hz ------------------Ans


Similar Questions:

Two cars P and Q are traveling along a motorway in the same direction. The leading car P travels at a steady speed of 12 m s⁻¹, the other car Q, traveling at a steady speed of 20 m s⁻¹, sound its horn to emit a steady note which P's driver estimates has a frequency of 830 Hz. What frequency does Q's own driver hear? (Speed of sound = 340 m s⁻¹) (Ans: 810 Hz)


A train sounds its horn before it sets off from the station and an observer waiting on the platform estimates its frequency at 1200 Hz. The trains then moves off and accelerates steadily. Fifty seconds after departure, the driver sounds the horn again and the platform observer estimates the frequency of 1140 Hz. Calculate the train speed 50 s after departure. How far from the station is the train after 50 s? (Speed of sound = 340 m s⁻¹). (Ans: 17.9 m s⁻¹, 448 m)




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