A sound detector is placed on a railway platform. A train, approaching the platform at a speed of `36 kmh^-1`, sounds its whistle. The detector detects 12.0 kHz is the most dominant frequency in the whistle. If the train stops at the platform and sounds the whistle, what would be the most dominant frequency detected? The speed of sound in air is `340 ms^-1`.

Explanation

Here the observer (detector) is at rest with respect to the mediam (air). Suppose the dominnt frequency as emitted by the train is `v_0`. When the trainn is at rest the platform, the detector will detect the domiN/Ant frequency frequency is `v_0`. Whenn this same train weas approachign the observer, the frequency detected was
`v'=v/(v-u_s)v_0`
or `v_0=(v-u_s)/v v'=(1-u_s/v)v'`
The speed of the source is
`u_s=36kmh^-1 (36xx10^3m)/(3600s)=10ms^-1` brgt Thus, `v_0=(1-10/340)xx12.0kHz`
`=11.6kHz`