Question 347: 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 ' V ' $\mathrm{m} / \mathrm{s}$, then the frequency of the sound reflected from the wall and as heard by the driver in Hz is

Accepted Answer

To solve this problem, we need to apply the Doppler effect twice:
First application:
As the car moves towards the wall, the wall acts as a stationary observer. The frequency of sound waves reaching the wall is given by the equation for a moving source:
$$ f' = \left( \frac{V}{V - V_1} \right) n $$
where:
$ f' $ is the frequency of the sound as heard by the wall,
$ V $ is the speed of sound,
$ V_1 $ is the speed of the car,
$ n $ is the original frequency of the siren.
Second application:
The wall reflects this frequency back towards the car, now acting as a source, and the car acts as a moving observer. The frequency of the reflected sound as heard by the driver can be calculated using:
$$ f'' = \left( \frac{V + V_1}{V} \right) f' $$
Substitute the expression for $ f' $ from the first application:
$$ f'' = \left( \frac{V + V_1}{V} \right) \left( \frac{V}{V - V_1} \right) n $$
Simplify the expression:
$$ f'' = \left( \frac{V + V_1}{V - V_1} \right) n $$
Thus, the frequency of the sound reflected from the wall and as heard by the driver is:
Option C:
$$ \left( \frac{V + V_1}{V - V_1} \right) n $$

Answer

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

Answer

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

Answer

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

Answer

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

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 ' V ' \mathrm{m} / \mathrm{s}, then the frequency of the sound reflected from the wall and as heard by the driver in Hz is

Choose the correct answer: