A stationary source emits a sound towards a wall moving towards it with a velocity u. speed of sound in in air = v. Find the fractional change in wavelength of the sound sent and the reflected sound.

Explanation

Let the frequency of the sound sent by the source be `f_(0)`
Frequency of sound as observed by the wall is
`:. F_(1) = f_(0) ((v + u)/(v)) f_(0)`
Frequency of the sound reflected by the wall is equal that received by it.
Now, the frequency `f_(2)` received by the source is
`f_(2) = ((v)/(v - u)) f_(1)`
`f_(2) = ((v)/(v - u) xx (v + u)/(v)) f_(0)`
`f_(2) = ((v)/(v - u)) f_(0)`
Initial wavelength `lambda_(1) = (v)/(f_(0))`
Final wavelength `lambda_(j) = (v)/(f_(2))`
Fractional charge in wavelength ` = (Delta lambda)/(lambda_(i)) = (-2u)/(v + u )`