Question

A sounding source of frequency 500 Hz moves towards a stationary observer with a velocity 30 m/s. If the velocity of sound in air is 330 m/s find the frequency heard by the observer.

• A. 500 Hz
• B. 550 Hz
• C. 355 Hz
• D. 55.5 Hz

Hint:

A sounding source of frequency 500 Hz moves towards a stationary observer with a velocity 30 m/s. If the velocity of sound in air is 330 m/s find the frequency heard by the observer.

Answer 1

The Correct Option is B

To determine the frequency heard by the observer when the source is moving towards them, we need to apply the Doppler effect formula for sound. The Doppler effect describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave.

The formula for the observed frequency \( f' \) when the source moves towards a stationary observer is given by:

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

Where:

• \(f'\) is the observed frequency.
• \(f\) is the source frequency (500 Hz in this case).
• \(v\) is the speed of sound in air (330 m/s).
• \(v_o\) is the speed of the observer (0 m/s, since the observer is stationary).
• \(v_s\) is the speed of the source towards the observer (30 m/s).

Substitute the given values into the formula:

\(f' = 500 \frac{330 + 0}{330 - 30}\)

\(f' = 500 \frac{330}{300}\)

\(f' = 500 \times 1.1\)

\(f' = 550 \text{ Hz}\)

Thus, the frequency heard by the observer is 550 Hz.

This calculation shows that the frequency increases when the source moves towards the observer, which is consistent with the principles of the Doppler effect.