Question

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

A

1 kg

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B

2 kg

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C

8 kg

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D

16 kg

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Solution

The correct option is B 16 kgso initially say load is m1 T = m1g v(velocity) =√Tμ = √m1gμ Fundamental frequency f = v4L f = √Tμ(14L) =√m1gμ(14L) On doubling the length f′ = √m2gμ × 1(8L) and changing load to m2 Question says f = f′ √m1gμ × 14L = √m2gμ × 18L m1gμ = 14 m2gμ 4m1 = m2 Load must be increased 4 times initial load was 4 kg (given). So now it should be 16 kg!

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