Question 204: Waves

Question

At what speed should a source of sound move so that the observer finds the apparent frequency equal to half the original frequency?

Accepted Answer

Step 1. Recall Doppler effect formula
When the
source
is moving (with constant velocity) and the observer is stationary, the apparent frequency $ f' $ is given by:
$ f' = f \cdot \frac{v}{v + v_s} $
where
$ f $ = actual frequency,
$ v $ = speed of sound in air,
$ v_s $ = speed of source (positive if source is moving
away
from observer).
Step 2. Condition given
We want the apparent frequency to be
half
the original:
$ f' = \frac{f}{2} $
Substitute in the formula:
$ \frac{f}{2} = f \cdot \frac{v}{v + v_s} $
Cancel $ f $:
$ \frac{1}{2} = \frac{v}{v + v_s} $
Step 3. Solve for $ v_s $
Cross multiply:
$ v + v_s = 2v $
$ v_s = v $
Step 4. Final Answer
The source should move with speed equal to the speed of sound $ V $.
Correct Option: D (V).
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Answer

$\frac{\mathrm{V}}{2}$

Answer

2 V

Answer

$\frac{\mathrm{V}}{4}$

Answer

V

Waves

At what speed should a source of sound move so that the observer finds the apparent frequency equal to half the original frequency?

Choose the correct answer: