In an experiment it was found that when a sonometer in its fundamental mode of vibration and a tunning fork gave `5` beats when length of wire is `1.05` metre or `1` metre. The velocity of transverse waves in sonometer wire when its length is `1m`

Options

A. `400m//s`
B. `210m//s`
C. `420m//s`
D. `450m//s`

Answer

C

Explanation

`n prop (1)/(l) implies(n_(1))/(n_(2))=(l_(2))/(l_(1))=(1)/(1.05)impliesn_(1)=(100)/(105)n_(2)`
`impliesn_(2) gt n_(1)`
Here fork gives `5` beats/sec with each length and hence `n_(2) gt n gt n_(1)`
`implies{:(n_(2)-n=5.....(1)),(ul(n-n_(1)=5).....(2)),(ul(n_(2)-n_(1)=10)):}`