Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of `72(km)/(h)` and `36(km)/(h)`. If second car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of first car when the line joining the cars makes angle of `45^@C` with the roads, will be (velocity of sound is `330(m)/(s)`)

Options

A. 321 Hz
B. 298 Hz
C. 289 Hz
D. 280 Hz

Answer

B

Explanation

The component of velocity of source along line joining the car is
`v_S=v_1cos45^@=36xx(1)/(sqrt2)(km)/(h)`
`=5sqrt2(m)/(s)`
component of velocity of observer (second car) along the line joining the car is
`v_0=v_2cos45^@=72xx(1)/(sqrt2)(km)/(h)`
`=10sqrt2(m)/(s)`
`n'=(v+v_0)/(v-v_S)n=(330+10sqrt2)/(330-5sqrt2)xx280`
`=(344)/(323)xx280Hz=298Hz`