A stationary source sends forth monochromatic sound. A wall approaches it with velocity 33 cm/s. The propagation velocity of sound in the medium is `c=330(m)/(s)`. How much, in per cent , does the wavelength of sound change on reflection from the wall?

Answer

decreases by `(2u)/((v + u)) = 0.2%`

Explanation

`f' = f(v + u)/(v)` Dopplar effect between source and wall
`f' = f"(v)/(v - u)` Dopplar effect after reflection
`f' = f"(v + u)/(v - u)`
`lambda' = (v)/(f') = (v(v - u))/(f(v + u)) = lambda(v - u)/(v + u)`
`(lambda'' - lambda)/(lambda) xx 100 = (lambda(v-u)/(v+u)-lambda)/(lambda)xx100 = (-2u)/(v+u)xx100 = (-2xx0.33)/(330xx0.33) approx -0.2%`