Question

Question #85ba3

Answer 1

The fundamental frequency of a streched string is given by the follwing formula.

`n=1/(2l)sqrt(T/m)`

Where

`l->"Length of the string"`

`T->"Tension of the string"`

`m->"Mass per unit length of the string"`

So T and m remaining constant

`nprop1/l`

let the frequency of the string is `n_1` when its length is 20cm and its frequency is `n_2` when its length is 21cm.
Si by the law of length

`n_1/n_2=21/20`

`Let" " n_1=21x Hzand n_2=20x Hz`

Let the frequency of tuning fork be `n_f` It forms 10 beats with both length of the sonometer string.

So `n_1 >n_f>n_2`

So
`n_1-n_f=10=>21x-n_f=10......(1)`

Again

`n_f-n_1=10=>n_f-20x=10......(2)`

Adding (1) and (2) we get
`x=20`

Inserting the value of x in (2)

`n_f-20*20=10`

`n_f=410Hz`

`"Hence frequency of tuning fork"=410Hz`