Question #85ba3

1 Answer
Aug 31, 2016

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#