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Question

Spacing between two successive nodes in a standing wave on a string is x. If tension in the string is doubled keeping frequency constant, then find the new spacing between successive nodes.

A
x2
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B
2x
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C
x2
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D
2x
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Solution

The correct option is A 2x

Spacing between successive nodes is x.
x=λ12
λ1=2x ..............(1)
Now, v=fλ
Here, frequency is kept fixed, so
λv
λTμ
λ2λ1=T2T1
(μ is same for string)
λ2λ1=2TTλ2=2λ1
New spacing between nodes is
x=λ22=2λ12
x=λ12
From equation (1)
x=2x2=2x
Hence, option (b) is the correct answer.

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