Question 109: Waves

Question

A wire having a linear mass density 9.0 $$	imes$$ 10$$-$$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ____________ m.

Accepted Answer

$$\mu  = 9.0 	imes {10^{ - 4}}{{kg} \over m}$$
T = 900 N
$$V = \sqrt {{T \over \mu }}  = \sqrt {{{900} \over {9 	imes {{10}^{ - 4}}}}}  = 1000$$ m/s
f
1
= 500 Hz
f = 550
$${{nV} \over {2l}} = 500$$ .... (i)
$${{(n + 1)V} \over {2l}} = 500$$ .... (ii)
(ii) (i) $${V \over {2l}} = 50$$
$$l = {{1000} \over {2 	imes 50}} = 10$$

Waves

A wire having a linear mass density 9.0 $\times 10-$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ____________ m.

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