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STD 11 - 14. waves and sound — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. waves and sound4 Marks
MCQ
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
  • A
    $x/\sqrt 2 $
  • ✓
    $\sqrt 2 x$
  • C
    $x/2$
  • D
    $2x$
✓

Answer

Correct option: B.
$\sqrt 2 x$
b
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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