Question

A string under a tension of 129.6 N produces 10 beats/ s when it is vibrated along with a tuning fork. When the tension in the string is increased to 160 N, it sounds in unision with the same tuning fork. Calculate the fundamental frequency of the tuning fork.

Answer 1

Suppose f be the frequency of the tuning fork. The frequency of the string will be either (f – 10) or (f + 10). With the increase in tension its frequency becomes f, so initial frequency of the string is (f – 10). Thus

After solving equations (i) and (ii), we get 

f = 100 Hz