A car P travelling at 20 \(ms^{–1}\) sounds its horn at a frequency of 400 Hz. Another car Q is travelling being the first car in the same direction with a velocity 40 \(ms^{–1}\) . The frequency heard by the passenger of the car Q is approximately [Take, velocity of sound = 360 \(ms^{–1}\) ]

Question

A passenger is sitting in a fast moving train. The engine of the train blows a whistle of frequency N. If the apparent frequency of sound heard by the passengers is \( N' \), then:

Answer 1

To solve this problem, we'll use the concept of relative motion and the Doppler effect for sound. The Doppler effect formula for sound when both the source and the observer are moving in the same direction is given by:

f' = f \left(\frac{v + v_o}{v + v_s}\right)

Where:

f' is the observed frequency.
f is the source frequency (400 Hz in this case).
v is the velocity of sound (360 ms^{-1}).
v_o is the velocity of the observer (car Q) which is 40 ms^{-1}.
v_s is the velocity of the source (car P) which is 20 ms^{-1}.

Since the observer is following the source, the observer's velocity is taken as positive. Plugging in the values:

f' = 400 \left(\frac{360 + 40}{360 + 20}\right)

Simplifying the terms inside the parenthesis:

f' = 400 \left(\frac{400}{380}\right)

Further simplifying:

f' = 400 \times \frac{10}{9.5} \approx 400 \times 1.0526 \approx 421.05

Thus, the frequency heard by the passenger of car Q is approximately 421 Hz.

Therefore, the correct answer is 421 Hz.

Answer 2