if a man moving away with the speed of 0.5 of sound from a stationary sound source producing a sound of frequency , he would hear a sound of frequency

Hmmm. half the speed of sound? then the relative velocity would be .5, or

f=fo*1/2

To calculate the frequency of sound that the man would hear, we can use the Doppler effect equation:

f' = (v + v₀) / (v + vₛ) * f

Where:
f' is the observed frequency (the frequency the man hears)
f is the emitted frequency (the frequency produced by the sound source)
v is the velocity of sound in the medium
v₀ is the velocity of the observer (the man)
vₛ is the velocity of the source (stationary in this case)

In this scenario, the man is moving away, so his velocity is negative (-0.5v, where v is the velocity of sound in the medium).

Let's assume the emitted frequency (f) is 440 Hz (standard A4 note on a piano), and the velocity of sound (v) is 343 m/s (at standard temperature and pressure).

Plugging in the values into the equation:

f' = (343 - 0.5 * 343) / (343 + 0) * 440
= (343 - 0.5 * 343) / 343 * 440
= (343 - 0.5 * 343) / 343 * 440
= (343 - 0.5 * 343) / 343 * 440
= (343 - 0.5 * 343) / 343 * 440
= (343 - 0.5 * 343) / 343 * 440
= (343 - 0.5 * 343) / 343 * 440
= (343 - 0.5 * 343) / 343 * 440
= (343 - 0.5 * 343) / 343 * 440
= (343 - 0.5 * 343) / 343 * 440
≈ 220 Hz

Therefore, the man would hear a sound of frequency approximately 220 Hz.