Question

A source of sound is moving towards a stationary observer with velocity 'V_s' and then moves away with velocity 'V_s'. Assume that the medium through which the sound waves travel is at rest, if 'V' is the velocity of sound and 'n' is the frequency emitted by the source, then the difference between the apparent frequencies heard by the observer is ______.

Options

• `(2"nV"  "V"_s)/("V"_s^2-"V"^2)`

• `("nV"  "V"_s)/("V"^2-"V"_s^2)`

• `("nV"  "V"_s)/("V"_s^2-"V"^2)`

• `(2"nV"  "V"_s)/("V"^2-"V"_s^2)`

Answer 1

A source of sound is moving towards a stationary observer with velocity 'V_s' and then moves away with velocity 'V_s'. Assume that the medium through which the sound waves travel is at rest, if 'V' is the velocity of sound and 'n' is the frequency emitted by the source, then the difference between the apparent frequencies heard by the observer is `underline((2"nV"  "V"_s)/("V"^2-"V"_s^2))`

Explanation:

`"n"_1="n""V"/("V"-"V"_s)`

`"n"_2="n""V"/("V"+"V"_s)`

`therefore"n"_1-"n"_2="n"["V"/("V"-"V"_s)-"V"/("V"+"V"_s)]`

`="nV"[("V"+"V"_s-"V"+"V"_s)/("V"^2-"V"_s^2)]`

`=(2"nV"  "V"_s)/("V"^2-"V"_s^2)`