A driver in a stationary car horns which produces monochromatic sound waves of frequency `n=1000Hz`, normally towards a reflecting wall. If the wall approaches the car will a velocity `u=3.3(m)/(s)`, calculate the frequency of sound reflected from wall and heard by the driver. What is the percentage change of sound frequency of reflection from the wall?

Explanation

Let S the stationary car and W the reflecting wall approaching with velocity u. `S'` is the image formed of S by the reflecting wall. IF reflecting surface moves with velocity u, the relative velocity of source and image is 2u. Therefore, it may be assumed that image `S'` approaches the stationary driver S with velocity 2u. Hence the apparent frequency is
`n'=(v)/(v-2u)n=(v)/(v(1-(2u)/(v))n=(1-(2u)/(v))^-n`
If `ultltv`, then
`n'=(1+(2u)/(v))n`
Here `u=3.3(m)/(s)`, `v=330(m)/(s)`, `n=1000`.
`n'=(1+(2xx3.3)/(330))xx1000=1020Hz`
percentage change in frequency is
`(n'-n)/(n)xx100%=(1020-1000)/(1000)xx100%=2%`