Question

When the wire of a sonometer is 73 cm long, it is in resonance with a tuning fork. On shortening the wire by 0.5 cm, it makes 3 beats with the same fork. Calculate the frequency of the tuning fork.

Answer 1

We are given that

L (original length of the wire) = 73 cm

L (shortened length of the wire) = (73 – 0.5) cm = 72.5 cm

Let v be the frequency of the tuning fork. 

This also is the frequency of the wire when its length is L as it is then in resonance with the tuning fork. Let v’ be the frequency of the wire when its length is L. Since it then produces 3 beats/s with the tuning fork, v = v + 3 

(On shortening the length, the frequency of the wire increases)

According to the law of length, 

vL = v L

or v x 73 = (v + 3) (72.5) = 72.5 v + 217.5

or 73 v – 72.5 v = 217.5 or 0.5 v = 217.5

v = 435 Hz