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Question
Choose the correct option:
A standing wave is produced on a string clamped at one end and free at the other. The length of the string ______.
Options
Must be an odd integral multiple of `lambda/4`
Must be an odd integral multiple of `lambda/2`
Must be an odd integral multiple of `lambda`
Must be an even integral multiple of `lambda`
Solution
A standing wave is produced on a string clamped at one end and free at the other. The length of the string must be an odd integral multiple of `lambda/4`.
Explanation:
The frequency (v) of a standing wave, fixed at one end and free at the other end is:
v = `((2n + 1)/2) v/(2L)`
Since V = `vlambda`
⇒ v = `(n + 1/2) (Vlambda)/(2L)`
⇒ L = `((2n + 1)/4)lambda`
⇒ L = `lambda/4, (3lambda)/4`,....
Therefore the length of the string is an odd integral multiple of `lambda/4`.
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