A tuning fork produces $6$ beats/sec with sonometer wire when its tensions are either $169 N$ or $196 N$ . The frequency of that fork is

162

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180

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200

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80

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Solution

The correct option is A $162$ Hz
The frequency of sound is given by
$f = \frac{\sqrt{\frac{T}{m / L}}}{2 L}$ . . . . . . . .(1)
where, $T =$ string tension
$L =$ string length
$m =$ string mass
From equation (1),
$f \propto \sqrt{T}$
Given, $f_{1} - f_{2} = 6 b e a t$
Lets consider, $f_{0} =$ frequency of the fork
$\frac{f + 6}{f - 6} = \sqrt{\frac{196}{169}} = 1.076$
$f + 6 = 1.076 (f - 6)$
$f + 6 = 1.076 f - 6.461$
$0.076 f - 12.461 = 0$
$f = \frac{12.461}{0.076}$
$f = 162 H z$
The correct option is A.

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A tuning fork produces 6 beats/sec with sonometer wire when its tensions are either 169N or 196N. The frequency of that fork is

A tuning fork produces $6$ beats/sec with sonometer wire when its tensions are either $169 N$ or $196 N$ . The frequency of that fork is