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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 B √2x Spacing between successive nodes is x. ⇒x=λ12 ⇒λ1=2x ..............(1) Now, v=fλ Here, frequency is kept fixed, so λ∝v ⇒λ∝√Tμ ⇒λ2λ1=√T2√T1 (∵μ is same for string) ⇒λ2λ1=√2T√T⇒λ2=√2λ1 New spacing between nodes is x′=λ22=√2λ12 ⇒x′=λ1√2 From equation (1) x′=2x√2=√2x Hence, option (b) is the correct answer.

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