Question

Spacing between two successive nodes in a standing wave on a string is x. If frequency of the standing wave is kept unchanged but tension in the string is doubled vibrating in the same harmonic, then new spacing between successive nodes will become

• A. x/√2
• B. √2x
• C. x/2
• D. 2x

Answer 1

Answer: (B)

√2x

Answer 2

spacing between successive nodes = $\frac{\lambda}{2}$ using V = nλ λ ∝ V

∝ $\sqrt{\frac{T}{\mu}}$

Now $\frac{\lambda'}{\lambda} = \frac{\sqrt{2T}}{\sqrt{T}}$

⇒ λ' = $\sqrt{2}T$

$\frac{\lambda'}{2} = \sqrt{2}.\frac{\lambda}{2}$

= √2 x