Question 298: Waves

Question

The driver of a car travelling with a speed ' $V_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall sounds a siren of frequency ' $n$ ' Hz. If the velocity of sound in air is $\mathrm{V} \mathrm{m} / \mathrm{s}$, then the frequency of sound reflected from the wall and as heard by the driver, in Hz , is

Accepted Answer

The car is moving toward the wall with a speed $$V_1$$ m/s and emits a sound with frequency $$n$$ Hz.
First, determine the frequency of the sound as received by the wall. Because the source (the car) is moving toward a stationary observer (the wall), the observed frequency is given by:
$$ f_{	ext{wall}} = \frac{V}{V - V_1} \, n $$
Here, $$V$$ is the speed of sound and $$V_1$$ is subtracted from $$V$$ because the source is moving toward the observer.
The wall reflects the sound. Essentially, the wall acts as a new source emitting sound at the frequency it received, which is $$f_{	ext{wall}}$$.
Now, the driver (moving toward the wall at speed $$V_1$$) hears the reflected sound. Since the driver is moving toward the stationary source (the wall), the frequency heard by the driver is increased further by:
$$ f_{	ext{observed}} = \frac{V + V_1}{V} \, f_{	ext{wall}} $$
Substitute $$f_{	ext{wall}}$$ from step 2:
$$ f_{	ext{observed}} = \frac{V + V_1}{V} \cdot \frac{V}{V - V_1}\, n = \frac{V + V_1}{V - V_1}\, n $$
Thus, the frequency of the reflected sound as heard by the driver is:
$$ \left(\frac{V + V_1}{V - V_1}ight) n $$
This corresponds to Option A.

Answer

$\left(\frac{\mathrm{V}+\mathrm{V}_1}{\mathrm{~V}-\mathrm{V}_1}\right) \mathrm{n}$

Answer

$\left(\frac{V-V_1}{V+V_1}\right) n$

Answer

$\left(\frac{V_1-V}{V_1+V}\right) n$

Answer

$\left(\frac{V_1}{V_1-V}\right) n$

Waves

The driver of a car travelling with a speed ' V_1 ' \mathrm{m} / \mathrm{s} towards a wall sounds a siren of frequency ' n ' Hz. If the velocity of sound in air is \mathrm{V} \mathrm{m} / \mathrm{s}, then the frequency of sound reflected from the wall and as heard by the driver, in Hz , is

Choose the correct answer: