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If the speed of the transverse wave in a wire under certain tension \(T\) is \(v\) , then its speed under tension \(2T\) (in ms-1 ) is

  • A.\(\frac{v}{\sqrt{2}}\)
  • B.\(2v\)
  • C.\(\sqrt{2}v\)
  • D.\(\frac{3v}{\sqrt{2}}\)
  • E.\(\frac{v}{2}\)

Answer: C

The speed becomes \(\sqrt{2}v\).

The speed of a transverse wave on a string is \(v = \sqrt{\frac{T}{\mu}}\), where \(\mu\) is the mass per unit length, which does not change.

\[ v' = \sqrt{\frac{2T}{\mu}} = \sqrt{2}\,v \]

2v treats the speed as proportional to the tension rather than its square root. \(\frac{v}{\sqrt{2}}\) and \(\frac{v}{2}\) make the wave slower under greater tension, which is backwards.

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