Is their any relationship between wave speed and the maximum partcle speed for a wave travelling on a string? If so, what is it?

A transverse wave is travelling on a string. The equation of the wave

The speed of transverse wave on a stretched string is

The speed of transverse wave on a stretched string is

A sinusoidal transverse wave is traveling on a string. Any point on the string

Mark out the correct statement (S) e.r.t. wave speed and particle velocity for a transverse travelling mechanical wave on a string.

Mark out the correct statement (S) e.r.t. wave speed and particle velocity for a transverse travelling mechanical wave on a string.

State the factors on which the speed of a wave travelling along a stretched ideal string depends.