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.
Answer (integer)
10
Solution
$\mu = 9.0 \times {10^{ - 4}}{{kg} \over m}$<br><br>T = 900 N<br><br>$$V = \sqrt {{T \over \mu }} = \sqrt {{{900} \over {9 \times {{10}^{ - 4}}}}} = 1000$$ m/s<br><br>f<sub>1</sub> = 500 Hz<br><br>f = 550<br><br>${{nV} \over {2l}} = 500$ .... (i)<br><br>${{(n + 1)V} \over {2l}} = 500$ .... (ii)<br><br>(ii) (i) ${V \over {2l}} = 50$<br><br>$l = {{1000} \over {2 \times 50}} = 10$
About this question
Subject: Physics · Chapter: Waves · Topic: Wave Motion and Types
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