A sonometer wire under tension of `128 N` vibrates in resonance with a tuning fork . The vibrating portion of sonometer wire has length of `20 cm` and mass ` 1 g`. The vibrating wire at constant speed of `0.75 m//s` and an observer standing near the sonometer hear ` 1 beat//s`. Find the speed of sound in air.

Answer

`300 m//s`

Explanation

Frequency of string
`f_(s) = (1)/( 2 L) sqrt((T)/( mu)) = (1)/(2) sqrt((T)/( ML))`
`= (1)/(2) sqrt ((128)/(10^(-3) xx 2 xx 10^(-1))) = 400 Hz`
When tuning fork is moved away from the observer standing near sonometer at constant speed of `0.75 m//s`. The apparent frequency of tuning fork.
` f_(1) = f_(s) ((v)/( v + 0.75)) = f_(s) (1 + (0.75)/(v))^(-1)`
` = f_(s) ( 1 - (0.75)/(v))`
`Delta f = f_(s) - f_(1) = f_(s) ((0.75)/(v)) , Delta f = 1`
`v = 300 m//s` (approximately)