Two sources of sound S1 and s2 are moving towards and away from a stationery observer with same speed respectively . Observer detects 3 beats per second. Find speed of sources (approximately) .
Given, F1=F2=500 Hz, speed of air = 330 m/s

Options

A. 1 m/s
B. 2 m/s
C. 3 m/s
D. 4 m/s

Answer

A

Explanation

`F=500 Hz " " F=500 Hz`
`S_(1) underset(V) to " Observer " S_(2) underset(V) to `
Beats = 3 beats/sec
`F_(1) =((330)/( 330-V))xx500 " " F_(2) =((330)/( 330+V))xx500`
Beats `=(F_(1)-F_(2))`
`3=((330)/(330-V)) xx 500 -((330)/(330+V))xx 500`
`3=(500)/( 330^(2) -V^(2)) xx 2V xx 330`
`V^(2) lt lt 330^(2)`
`3=(500 xx 300 xx 2V)/(330^(2))`
`V=(3xx 330)/(2xx 500) rArr V=0.99m//s = "approx " 1 m//s`