Question

The observer is moving with velocity 'v₀' towards the stationary source of sound and then after crossing moves away from the source with velocity 'v₀'. 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 apparent frequencies heard by the observer is ______.

विकल्प

• `(2"nv"_0)/"v"`

• `"nv"_0/"v"`

• `"v"/(2"nv"_0)`

• `"v"/("nv"_0)`

Answer 1

The observer is moving with velocity 'v₀' towards the stationary source of sound and then after crossing moves away from the source with velocity 'v₀'. 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 apparent frequencies heard by the observer is `underlinebb((2"nv"_0)/"v")`.

Explanation:

From the Doppler effect, the apparent frequency increases when the observer is moving towards the source while the source is stationary.

n' = n `(("v"+"v"_0)/"v")`                  ...(i)

The apparent frequency appears when the observer is moving away from the source while the source is still.

n" = `-"n"(("v"-"v"_0)/"v")`             ...(ii)

From eqs. (i) and (ii),

n' - n" = `"n"/"v"`(v + v₀ - v + v₀) 

= `(2"nv"_0)/"v"`