Question

14-14. For a science experiment, you would like to use the Doppler effect to double the perceived frequency of a harmonica, from the 261.7-Hz tone (middle C) that it emits, to 493.9 Hz (B4 note).

a) Calculate the speed the harmonica must have in order for a stationary observer to hear 493.9 Hz.

b)Calculate the speed an observer must have in order to perceive a 493.9-Hz sound from a stationary harmonica that emits sound at 261.7 Hz.

Answer 1

14A.

Using Doppler's effect

when source is moving towards an stationary observer:

f1 = f0*V/(V - Vs)

V = Speed of sound at room temperature = 343 m/sec

Vs = speed of Source = ?

f0 = frequency of harmonica = 261.7 Hz

f1 = frequency heard by observer = 493.9 Hz

So,

V - Vs = f0*V/f1

Vs = V - f0*V/f1

Using given values:

Vs = 343 - 261.7*343/493.9

Vs = Speed of harmonica = 161.3 m/sec

Part B.

Now when Observer is moving towards stationary Source

f1 = f0*(V + Vo)/V

Vo = Speed of observer

V + Vo = f1*V//f0

Vo = (f1*V/f0) - V

Using known values:

Vo = (493.9*343/261.7) - 343

Vo = 304.33 m/sec = Speed of observer

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