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Need for Intensity

A string of l...

Question

A string of length $l$ fixed at both ends vibrates in its fundamental mode and transverse waves travel along the string with a velocity $V$ . Sound waves travel in the air with velocity $v$ . What is the wavelength in air of the sound produced by this string?

A

\frac{2 l v}{V}

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B

\frac{2 l V}{v}

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C

\frac{l V}{v}

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D

2 l

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Solution

The correct option is A $\frac{2 l v}{V}$
$F r e q u e n c y o f s o u n d p r o d u c e d b y s t r i n g = n = \frac{V}{2 l} W a v e l e n g t h o f s o u n d i n a i r = \frac{v}{n} = \frac{v}{(V / 2 l)} = \frac{2 l v}{V}$

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