Two sound waves of wavelengths 85/133 m and 85/137 m when sounded together produce 8 beats/s with a third note of fixed frequency then the frequency of third note will be

Options

A. 532 Hz
B. 540 Hz
C. 680 Hz
D. 340 Hz

Answer

B

Explanation

`n_(2) - n = 8 and n - n_(1) = 8`
`:. n_(2) - n_(1) = 16`
`(v)/(lamda_(2)) - (v)/(lamda_(1)) = 16 " " :. v [(137)/(85) - (133)/(85)] = 16`
`4v = 16 xx 85 :. v = 4 xx 85 = 340 m//s`
`v = n_(1) lamda_(1) :. n_(1) = (v)/(lamda_(1)) = (340)/(85) xx 133 = 532`
`n = n_(1) + 8 " " :. 532 + 8 = n`
`n = 540 Hz`