A source of sound is moving with a velocity of `50ms^(-1)` towards a stationary observer . The Observer measure the frequency of sound as 500Hz. The appartment frequency of sound as heard by the observer when source is moving away from hom with the same speed is (Speed of sound at room temperature `350ms^(-1)`

Options

A. 400 Hz
B. 666 Hz
C. 375 Hz
D. 177.5 Hz

Answer

C

Explanation

`v_(L)=0,v_(s)=-50ms^(-1),f_(app)=500Hz` (source towards the listener)
`f_(app)^(1)=?` (source away from the listener)
`v=v_("sound")=350ms^(-1)`
General formula: `f_(app)=f_("true")((v+v_(L))/(v+v_(s)))`
Convention L = listener (observer)
s = source
Case (i) : Source towards the listener
`f_(app)=f_("true")((v+0)/(v+v_(s)))" "....(1)`
Case (ii) : Source away from the listener
`f_(app)=f_("true")((V+1)/(V+V_(S)))" "....(2)`
`((1))/((2))implies(f_(app))/(f._(app))=(v+v_(s))/(v-v_(s))`
`(500)/(f._(app))=(350+50)/(350-50)=(400)/(300)=(4)/(3)`
`f._(app)=500xx(3)/(4)=375Hz`