Wave Motion 4 Question 5

5. Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20ms1 with respect to the ground. If an observer in car A detects a frequency 2000Hz of the sound coming from car B, what is the natural frequency of the sound source in car B ? (speed of sound in air =340ms1 )

(2019 Main, 9 April II)

(a) 2060Hz

(b) 2250Hz

(c) 2300Hz

(d) 2150Hz

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Solution:

  1. The given condition can be shown below as,

Here, source and observer both are moving away from each other. So, by Doppler’s effect, observed frequency is given by

f=f0(v+vovvs)

where, v= speed of sound =340ms1,

vo= speed of observer =20ms1,

vs= speed of source =20ms1,f0= true frequency 

and f= apparent frequency =2000Hz

Substituting the given values in Eq. (i), we get

2000=(34020340+20)×f0f0=2000×360320=2250Hz



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