Question 220: Waves

Question

A metal wire of linear mass density of $$9.8$$ $$g/m$$ is stretched with a tension of $$10$$ $$kg$$-$$wt$$ between two rigid supports $$1$$ metre 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 $$n.$$ The frequency $$n$$ of the alternating source is

Accepted Answer

KEY CONCEPT :
For a string vibrating between  two rigid support, the fundamental frequency is given by
$$n = {1 \over {2\ell }}\sqrt {{T \over \mu }}  = {1 \over {2 	imes }}\sqrt {{{10 	imes 9.8} \over {9.8 	imes {{10}^{ - 3}}}}}  = 50Hz$$
As the string is vibrating in resonance to a.c of frequency $$n,$$ therefore both the frequencies are same.

Answer

$$50$$ $$Hz$$

Answer

$$100$$ $$Hz$$

Answer

$$200$$ $$Hz$$

Answer

$$25$$ $$Hz$$

Waves

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