## Question

A metal wire of diameter 1 mm is held on two knife edges separated by a distance of 50 cm. The tension in the wire is 100 N. The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce 5 beats per second. The tension in the wire is then reduced to 81 N. When the two are excited, beats are heard at the same rate. What is the frequency of the fork?

### Solution

95 Hz

Let *N* be the frequency of the tuning fork. Then, the frequency of the wire, when the tension is 100 *N* will be (*N* + 5) and when the tension is 81 *N*, it is (*N* – 5); since in each case 5 beats are heard per second. Hence

subtracting (ii) from (i) we have

Using this value of *m* in (i) or (ii) gives *N* = 95 Hz.

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