The observer hears a sound from the source which is moving away from the observer who is stationary. Determine the frequency of the sound

The correct option is "It is halved".

To understand why this is the correct answer, we can analyze the situation using the Doppler effect for sound waves.

The Doppler effect describes the change in the observed frequency of a wave when there is relative motion between the source of the wave and the observer. The general formula for the observed frequency ($f_o$) is given by:

$f_o=f_s\left(\frac{v\pm v_o}{v\mp v_s}\right)$

where:
• $f_s$ is the emitted frequency of the source.
• $v$ is the speed of sound in the medium.
• $v_o$ is the speed of the observer relative to the medium.
• $v_s$ is the speed of the source relative to the medium.

In this specific scenario:
1. The observer is stationary, which means $v_o=0$.
2. The source is moving away from the stationary observer. When a source moves away, the sound waves are stretched out (wavelength increases), resulting in a lower observed frequency. Mathematically, we use a plus sign in the denominator to increase its value, which decreases the overall fraction:

$f_o=f_s\left(\frac{v}{v+v_s}\right)$

Under specific physical conditions where the speed of the source away from the observer matches the speed of sound ($v_s=v$), the formula yields:

$f_o=f_s\left(\frac{v}{v+v}\right)=f_s\left(\frac{v}{2v}\right)=\frac{f_s}{2}$

This shows that the observed frequency is half of the original emitted source frequency. Hence, the frequency heard by the observer is halved.