A child is swinging back and forth with a constant period and amplitude. Somewhere in front of the child, a stationary horn is emitting a constant tone of frequency fs Five points are labeled in the drawing to indicate positions along the arc as the child swings. At which position(s) will the child hear the lowest frequency for the sound from the whistle?

Explanation:

  We shall apply concept of Doppler's effect of apparent frequency to this problem . Here observer is moving sometimes towards and sometimes away from the source . When observer moves towards the source , apparent frequency is more than real frequency and when the observer moves away from the source , apparent frequency is less than real frequency . The apparent frequency depends upon velocity of observer . The formula for apparent frequency when observer is going away is as follows .

f = f₀ ( V - v₀ ) / V , f is apparent , f₀ is real frequency , V is velocity of sound and v is velocity of observer .

f will be lowest when v₀ is highest .

velocity of observer is highest when he is at the equilibrium position or at middle point .

So apparent frequency is lowest when observer is at the middle point and going away from the source  while swinging to and from before the source of sound .

the area between the graph and the t axis

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