A wire having tension 225 N produces six beats per second when it vibrates with some tuning fork. When the tension changes to 256 N , it vibrates with the same fork with the number of beats remaining

Question

A wire having tension 225 N produces six beats per second when it vibrates with some tuning fork. When the tension changes to 256 N , it vibrates with the same fork with the number of beats remaining unchanged. The frequency of the fork will be

TestHub · Accepted Answer

For wire vibrating under tension, the fundamental frequency is given by

$f_{1} = \frac{1}{2 L} \sqrt[]{\frac{T}{μ}}$ , Where T is tension and $μ$ linear mass density of string
It is given that, when it is sounded with a tuning fork of frequency $x$ , $6$ beats per second were heard

$∴ (x - f) = 6$

$f_{1} = \frac{1}{2 L} \sqrt{\frac{225}{μ}}$

$f_{2} = \frac{1}{2 L} \sqrt{\frac{256}{μ}}$ undefined

$∴ (x + 6) = \frac{16}{15} (x - 6)$

$∴ 15 x + 90 = 16 x - 96$

$∴ x = 186 H z$

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