Question

A person sitting on a bench hears the sound of a truck moving away at a speed of $10{\text{m s}}^{-1}$. If the frequency of the sound produced by the truck is $300\text{Hz}$, what is the percentage change in the frequency of the sound (in seconds) perceived by the person? (velocity of sound in air $\approx 350{\text{m s}}^{-1}$)

• A. $-2.78\%$
• B. $+2.78\%$
• C. $+3.24\%$
• D. $-3.24\%$

Answer 1

The correct option is A $-2.78\%$

Given:
The velocity of sound in air, $\text{v}=350{\text{m s}}^{-1}$
The speed of the source of sound (truck), ${\text{v}}_{\text{s}}=10{\text{m s}}^{-1}$
The actual frequency of the sound, $\text{f}=300\text{Hz}$

If $\text{f *}$ is the apparent frequency, then in this case:

$\text{f *}=\left(\frac{\text{v}}{\text{v +}{\text{v}}_{\text{s}}}\right)\text{f}$

$⟹\left(\frac{350}{350+10}\right)\times 300$

$⟹\frac{350}{360}\times 300=\frac{875}{3}$

$⟹291.67\text{Hz}$

Change in the frequency, $\frac{\Delta \text{f}}{\text{f}}=\frac{\text{f *}-\text{f}}{\text{f}}=\frac{291.67-300}{300}=\frac{-1}{36}$
$\therefore \%\frac{\Delta \text{f}}{\text{f}}=\frac{-1}{36}\times 100=-2.78\%$