A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with a fundamental frequency of 600 Hz under the same tension is ____ cm.

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Solution

Q.
A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with a fundamental frequency of 600 Hz under the same tension is ____ cm. [2024]

Ans.
(60)

$f_{0} = 400 Hz; v = \sqrt{\frac{T}{μ}} = constant$

$\frac{λ}{2} = L; v = f_{0} λ$

$\frac{v}{2 f_{0}} = L \Rightarrow v = 2 L f_{0}$

$L' = \frac{v}{2 f'} = \frac{2 L f_{0}}{2 f'}$

$= \frac{L f_{0}}{f'} = \frac{90 \times 400}{600} = 60$

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