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Matter Waves

If the tensio...

Question

If the tension in a string is doubled and its linear density is halved, then the velocity of the wave in the string

A

Is quadrupled

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B

Is halved

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C

Remains constant

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D

Is doubled

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Solution

The correct option is D Is doubled
Velocity of the wave in the string is, $v = \sqrt{\frac{T}{m / L}}$ where, T is the tension of the string, m is the mass of it and L is the length. Here we have done, $T_{f i n a l} = 2 T$ and $(m / L)_{f i n a l} = 0.5 (m / L)$ . So using the above formula, the $v_{f i n a l} = 2 v$ .

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