In an experiment with sonometer, when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. [2023]

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Solution

Q.
In an experiment with sonometer, when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is ______ g. [2023]

Ans.
(500)

$f = \frac{1}{2 ℓ} \sqrt{\frac{T}{μ}} (T : Tension)$

$\frac{f_{2}}{f_{1}} = \sqrt{\frac{T_{2}}{T_{1}}}$

${(\frac{50}{30})}^{2} = \frac{m g}{180 g}$ $\Rightarrow m = \frac{25}{9} \times 180 = 500 gram$

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