Question

The speed of transverse wave in taut string is V. What will be the speed of transverse wave in that string if tension is kept unchanged and the length of the string is increased by 4 times ?

Answer 1

The equation for the wave speed in a string is

$$v=\sqrt{\frac{TL}{m}}.$$

What will be the new speed if we increase the length 4 times?

$$u=\sqrt{\frac{4LT}{m}}=2\sqrt{\frac{TL}{m}}=2v.$$

Thus, wave speed will increase twice.

Note: Of course, this will be true only if the mass of the string remains unchanged, like we "stretch" the string.