Question 254: Waves

Question

An observer moves towards a stationary source of sound with a velocity of one fifth of the velocity of sound. The percentage increase in the apparent frequency is

Accepted Answer

Step 1. Recall Doppler Effect for sound
When
observer moves towards source
:
$ f' = f \left( \frac{v + v_o}{v} ight) $
$f$: actual frequency
$f'$: apparent frequency
$v$: velocity of sound
$v_o$: velocity of observer towards source
Step 2. Substitute values
Observer velocity is $v_o = \frac{1}{5} v$.
$ f' = f \left( \frac{v + 	frac{1}{5} v}{v} ight) = f \left( 1 + \frac{1}{5} ight) = f \left( \frac{6}{5}ight) $
Step 3. Percentage increase
Increase in frequency:
$ \Delta f = f' - f = \frac{6}{5}f - f = \frac{1}{5}f $
So percentage increase:
$ \frac{\Delta f}{f}	imes 100\% = \frac{1}{5}	imes 100\% = 20\% $
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Answer: Option C Ã¢ÂÂ $20\%$

Answer

$5 \%$

Answer

$10 \%$

Answer

$20 \%$

Answer

$25 \%$

Waves

An observer moves towards a stationary source of sound with a velocity of one fifth of the velocity of sound. The percentage increase in the apparent frequency is

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