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  4. A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to

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Q. A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency $416 Hz$. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to

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Solution:

For a sonometer, $v_{\text {fundamental }}=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$
To maintain the fundamental mode, on doubling the length, tension must be quadrupled.