A car sounding a horn of frequency 1000 Hz passes an observer. The ratio of frequencies of the horn noted by the observer before and after passing of the car is 11 : 9. If the speed of sound is v , the speed of the car is

Options

A. v
B. `(1)/(2)v`
C. `(1)/(10)v`
D. `(1)/(5)v`

Answer

C

Explanation

The apparent frequency heard by the observer before and after passing of the car are given by
`n_(1) = ((v)/(v- v_(s))) n and n_(2) = ((v)/(v + v_(s)))n`
where v is the speed of the sound
`:. (n_(1))/(n_(2)) = (11)/(9) = (v + v_(s))/(v - v_(s))`
`:. 11v - 11v_(s) = 9v + 9v_(s)`
`:. 2v = 20v_(s) " " :. v_(s) = (v)/(10)`