Question

Wire having tension 225N produces six beats per second when it is tuned with the fork. when tension changes to 256 N, it is tuned with the same fork the number of Beats remain unchanged the frequency of the fork will be ​

Answer 1

you know as well frequency of tuning fork is directly proportional to square root of tension applied on it.

e.g., $f\propto\sqrt{T}$

or, f = k√T

case 1 :- wire having tension 225N produces six beats per second.

Let f is initial frequency of tuning fork.

so, f - k√225 = 6

or, f - 6 = k√225 = 15k .....(1)

case 2 : when tension changes to 256 N, it is tuned with the same fork the number of Beats remain unchanged the frequency of the fork.

so, f + 6 = k√256 = 16k .....(2)

from equation (1) and (2),

(f - 6)/(f + 6) = 15/16

or, 16(f - 6) = 15(f + 6)

or, 16f - 96 = 15f + 90

or, f = 186 Hz

hence, initial frequency of tuning fork is 186 Hz.