two waves of wavelength 100 cm and 102 cm produce 12 beats per second having same velocity. the velocity of each wave is

Options

A. `303 ms^-1`
B. `332 ms ^-1`
C. `323.2 ms ^-1`
D. `300 ms^(-1)`

Answer

C

Explanation

Frequency of fundamental mode of vibrations of `1^(st)` closed organ pipe .
`v_(1)= (v)/(4 l_(1)) = (v)/(4 xx 100) " " …. (i) `
Frequency of fundamental mode of vibrations of `2^nd` closed organ pipe .
`v_(2) = (v)/(4l_(2)) = (v)/(4 xx 101) " " ... (ii)`
From question , `v_(1) - v_(2) = (16)/(20)`
`implies (v)/(4 xx 100) - (v)/(4 xx 101) = (16)/(20)`
`implies (v)/(4)* [(1)/(100) - (1)/(101)] = (16)/(20)`
`implies (v)/(4)[(101 - 100)/(101)] = (16)/(20) implies (v)/(4) xx (1)/(101) = (16)/(20)`
`implies v = (16 xx 101 xx 4)/(20) = 323.2 m//s`.