Question

A metal wire of linear mass density of 9.8/gm is stretched with a tension of 10kg wt between two rigid supports 1m apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance, when carrying an alternating current of frequency v. The frequency v of the alternating source is?

(a) 50 Hz

(b) 100 Hz

(c) 200 Hz

(d) 25 Hz

I have been asked this question in a job interview.

Query is from Longitudinal Waves topic in section Waves of Engineering Physics I

Answer 1

Correct option is (a) 50 Hz

To explain: Here, m=9.8/gm=9.8×10^-3 kg/m

T=10kg wt = 9.8×10=98N

L=1m

The fundamental frequency of vibration of the string,

v=1/2L×√(T/m)=1/2×√(9.8/(9.8×10^-3))=50Hz.