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A stretched string resonates with tuning fork frequency 512 Hz when length of the string is 0.5 m. The length of the string required to vibrate resonantly with a tuning fork of frequency 256 Hz would be

1. 0.25 m
2. 0.5 m
3. 1 m
4. 2 m

Correct answer: 1 m

Solution

The frequency of a stretched string is inversely proportional to its length when tension and other factors are constant. Halving the frequency (from 512 Hz to 256 Hz) requires doubling the length of the string, so the new length is 1 m.

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