Question 357: Waves

Question

A source of sound is moving towards a stationary observer with $$\left(\frac{1}{10}ight)^{	ext {th }}$$ the of the speed of sound. The ratio of apparent to real frequency is

Accepted Answer

The frequency of the sound as perceived by an observer when the source of sound is moving towards the observer is given by the Doppler Effect. According to the Doppler Effect, if a source of sound with the frequency $$f_0$$ (real frequency) moves towards a stationary observer with velocity $$v_s$$ and the sound travels with a velocity $$v$$, then the apparent frequency $$f'$$ heard by the observer is given by:
$$ f' = f_0 \left(\frac{v + v_0}{v - v_s}\right) $$
Here, $$v_0$$ is the velocity of the observer which is zero and $$v_s = \frac{v}{10}$$ since the source of sound is moving at one tenth the speed of sound. Substituting these values back into the equation, we get:
$$ f' = f_0 \left(\frac{v}{v - \frac{v}{10}}\right) $$
$$ f' = f_0 \left(\frac{v}{\frac{9v}{10}}\right) $$
$$ f' = f_0 \left(\frac{10}{9}\right) $$
Hence, the ratio of the apparent frequency to the real frequency is $$10:9$$, which corresponds to Option A.

Answer

$$10: 9$$

Answer

$$11: 10$$

Answer

$$(11)^2:(10)^2$$

Answer

$$(9)^2:(10)^2$$

Waves

A source of sound is moving towards a stationary observer with $\left(\frac{1}{10}\right)^{\text {th }}$ the of the speed of sound. The ratio of apparent to real frequency is

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