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Q.

A wire whose linear density is 5 × 10^-3 kg/m is stretched between two points with a tension 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. What is the length of the wire?

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a

1.2 m

b

1.8 m

c

8.1 m

d

2.1 m

answer is C.

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Detailed Solution

In strings the difference between two successive frequencies equal to fundamental frequency (n)
$n = 70 Hz ∴ n = \frac{1}{2 l} \sqrt{\frac{T}{m}} \Rightarrow 70 = \frac{1}{2 l} \sqrt{\frac{450}{5 x 10^{- 3}}}; l = \frac{1}{2} x \frac{1}{70} \sqrt{90000} = 2.1 m$

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