A train is moving at `30 m//s` in still air. The frequency of the locomotive whistle is `500 Hz` and the speed of sound is `345 m//s`. The apparent wavelengths of sound in front of and behind the locomotive are respectively

Options

A. `0.63 m, 0.80 m`
B. `0.63 m, 0.75 m`
C. `0.60 m, 0.85 m`
D. `0.60 m, 0.75 m`

Answer

B

Explanation

`{:(rarr v_(o) = 0,rarrv_(s) = 30m//s,rarr v_(o) = u),(overset(*)(O_(2)),overset(*)(S),overset(*)(O_(1))):}`
Frequency received by `O_(1), f_(1) = f((v)/(v-v_(s)))`
`(v)/(lambda_(1)) = f((v)/(v-v_(s)))`
`lambda_(1) = (v-v_(s))/(f) = (345 - 30)/(500) = 0.63 m`
Frequency received by `O_(2), f_(2) = f((v)/(v+v_(s)))`
`(v)/(lambda_(2)) = f((v)/(v+v_(s)))`
`lambda_(2) = (v+v_(s))/(f) = (345+30)/(500) = 0.75 m`