Speed of wave on a wire of length L and mass M is:

$\overline{){\mathbf{v}}{\mathbf{=}}\sqrt{\frac{\mathbf{M}\mathbf{g}\mathbf{L}}{\mathbf{m}}}}$

**A.**

Suppose the mass M is doubled, the speed of the wave on the wire is now:

v' = sqrt[(2M)gL/m]

When a mass M hangs from a vertical wire of length L, waves travel on this wire with a speed V.

A. What will be the speed of these waves (in terms of V) if we double M without stretching the wire?

B. What will be the speed of these waves (in terms of V) if we replace the wire with an identical one, except twice as long?

C. What will be the speed of these waves (in terms of V) if we replace the wire with one of the same length, but three times as heavy?

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