A source of sound `S` emitting waves of frequency `100 Hz` and an observer `O` are located at some distance from each other. The source is moving with a speed of `19.4ms^-1` at an angle of `60^(@)` with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air `330ms^-1`) is

Options

A. 106 Hz
B. 97 Hz
C. 100 Hz
D. 103 Hz

Explanation

Here,
Frequency of source, `upsilon_(0)=100Hz` Velocity of source, `v_(s)=19.4ms^(-1)` Velocity of sound in air, `v=330ms^(-1)` As the velocity of source along the source observer line is `v_(s)cos60^(@)` and the observer is at rest, so the apparent frequency observed by the observer is
`upsilon=upsilon_(0)((v)/(v-v_(s)cos60^(@)))`
`=(100Hz)((330ms^(-1))/(330ms^(-1)-(19.4ms^(-1))((1)/(2))))=103Hz`