A wire is in uniform with a tuning fork when stretched by a weight of density `9000 kg//m^(3)` in a sonometer experiment . When the weight is immersed in water , the same wire produces ` 5 beats//s` with the same fork. Find the frequency of the fork.

Options

A. `78.8 Hz`
B. `86 Hz`
C. `80 Hz`
D. `87.4 Hz`

Answer

D

Explanation

`n = (1)/( 2l) sqrt((W)/(m))`
where `W =` weight of load in air
`n' = (1)/( 2I) sqrt((W')/(m))`
where ` W' =` weight of load in water
Obviously ` n' lt n or n "because" W' lt W`
`:. N - n' = 5 or n' = n - 5 `
or `((n)/( n - 5))^(2) = (W)/( W')`
`W = V( 9000 )g`
`W' = W - B`
` = V(9000)g - V ( 1000)g`
`= V ( 8000)g`
So `(W)/(W') = (9)/( 8)`
`:. (9)/(8) = ((n)/( n - 5 ))^(2) or n = 87. 4 Hz`