Question

A person sitting on a bench hears the sound of a truck moving away at a speed of $45\text{kmph}$. If the frequency of the sound produced by the truck is $125\text{Hz}$, what is the apparent time period of the sound (in seconds) perceived by the person? (Velocity of sound in air = $350{\text{m s}}^{-1}$)

• A. 0.008286

Answer 1

The correct option is A 0.008286
Given:
The velocity of sound in air, $\text{v}=350{\text{m s}}^{-1}$
The speed of the source of sound (truck), ${\text{v}}_{\text{s}}=45\text{kmph}$

$=45\times \frac{5}{18}=12.5{\text{m s}}^{-1}$

The actual frequency of the sound, $\text{f}=125\text{Hz}$
If $\text{f *}$ is the apparent frequency, then:
$\text{f *}=\left(\frac{\text{v}}{\text{v +}{\text{v}}_{\text{s}}}\right)\text{f}$

$⟹\left(\frac{350}{350+12.5}\right)\times 125$

$⟹120.69\text{Hz}$

The apparent time period:
$\left(\text{t *}\right)=\frac{1}{\text{f *}}=\frac{1}{120.69}$

$⟹0.008286\text{s}$