Question 309: Waves

Question

With what velocity an observer should move relative to a stationary source so that a sound of triple the frequency of source is heard by an observer?

Accepted Answer

To determine the velocity at which an observer should move relative to a stationary sound source to hear a sound at triple the frequency of the source, we can use the Doppler effect formula for sound:
$$ f' = f \left( \frac{v + v_o}{v} \right) $$
where:
$ f' $ is the observed frequency,
$ f $ is the source frequency,
$ v $ is the velocity of sound in the medium,
$ v_o $ is the velocity of the observer (positive if moving towards the source).
Given that $ f' = 3f $, we have:
$$ 3f = f \left( \frac{v + v_o}{v} \right) $$
Simplifying the equation:
$$ 3 = \frac{v + v_o}{v} $$
Multiply both sides by $ v $:
$$ 3v = v + v_o $$
Subtract $ v $ from both sides:
$$ 2v = v_o $$
Thus, the observer should move with a velocity $ v_o = 2v $ towards the source. Therefore, the correct option is:
Option D: Twice the velocity of sound towards the source.

Answer

Same as velocity of sound towards the source.

Answer

Same as velocity of sound away from the source.

Answer

Half the velocity of sound towards the source.

Answer

Twice the velocity of sound towards the source.

Waves

With what velocity an observer should move relative to a stationary source so that a sound of triple the frequency of source is heard by an observer?

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