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, then new spacing between successive nodes will become
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Spacing between successive nodes $=\frac{\lambda}{2}$ using $\mathrm{V}=\mathrm{n} \lambda$
$\lambda \propto V \propto \sqrt{\frac{T}{\mu}}$
New $\frac{\lambda^{\prime}}{\lambda}-\frac{\sqrt{2 T}}{\sqrt{T}} \Rightarrow \lambda^{\prime}=\sqrt{2} \lambda$
$\frac{\lambda^{\prime}}{2}=\sqrt{2} \cdot \frac{\lambda}{2}=\sqrt{2} \mathrm{x}$ Ans.
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