Question

A bat, flying at 5.9 m/s, pursues an insect that is flying at 1.9 m/s in the same direction. The bat emits a 47000-Hz sonar pulse. Take the speed of sound to be 343 m/s.

At what frequency, in hertz, does the bat hear the pulse reflected back from the insect?

Answer 1

Using doppler's effect:

frequency received by insect will be, when Source is moving towrds observer and observer is moving away from source.

f1 = f0*(V - Vo)/(V - Vs)

f0 = frequency emits by bat = 47000 Hz

V = Speed of Sound = 343 m/sec

Vo = speed of Object(insect) = 1.9 m/sec

Vs = speed of source(bat) = 5.9 m/sec

f1 = 47000*(343 - 1.9)/(343 - 5.9) = 47557.7 Hz

Now frequency reflected by insect will be:

f2 = f1*(V + Vo)/(V + Vs)

here,

Vo = speed of Object(bat) = 5.9 m/sec

Vs = speed of source(insect) = 1.9 m/sec

Using above value of f1

f2 = 47557.7*(343 + 5.9)/(343 + 1.9)

f2 = frequency received by bat = 48109 Hz

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