A source of sound with natural frequency `f_0=1800Hz` moves uniformly along a straight line separated from a stationary observer by a distance `l=250m`. The velocity of the source is equal to `eta=0.80` fraction of the velocity of the sound.
Q. The distance between the source and the observer at the moment when the observer receives a frequency `f=f_0` is

Options

A. `640m`
B. `420m`
C. `320m`
D. `250m`

Answer

A

Explanation

When the source is at point C its velocity of approach towards the stationary observer is zero. Therefore, when the sound wave emitted by the source from C reaches the observer `((l)/(v)`time later) the observed frequency will be `f_0` in the same time interval `((l)/(v))` the source will have moved a distance say `CD=(etav)((l)/(v))=etal`. At this moment, the distance between the source and observer is
`OD=sqrt(OC^2+CD^2)`
`=sqrt(l^2+eta^2l^2)=lsqrt(1+eta^2)`
`=250sqrt(1+(0.8)^2)=320`m