Wave Motion 4 Question 4

4. A stationary source emits sound waves of frequency 500Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480Hz and 530Hz. Their respective speeds are in ms1,

(Take, speed of sound =300m/s )

(2019 Main, 10 April I)

(a) 12,16

(b) 12,18

(c) 16,14

(d) 8,18

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Solution:

  1. Given,

Frequency of sound source (f0)=500Hz Apparent frequency heard by observer 1,f1=480Hz and apparent frequency heard by observer 2,f2=530Hz.

Let v0 be the speed of sound.

When observer moves away from the source, Apparent

frequency, f1=f0(vv0v)

When observer moves towards the source,

Apparent frequency, f2=f0(v+v0v)

Substituting values in Eq. (i), we get

480=500(300v0300)

96×3=300v0v0=12m/s

Substituting values in Eq. (ii), we get

530=500(330+v300)106×3=300+vv0=18m/s

Thus, their respective speeds (in m/s ) is 12 and 18 .



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