Question

prove that if a transverse wave is travelling on the string then the slope at any point is numerically equal to the ratio of wave speed and particle speed

Answer 1

Equation of transverse is Y= Asin(kx-wt). So when it is differentiated, it comes concerning t, and by differentiating, we get wACos (Kx-wt)

Cos)kx-wt)=1

So dy/dt- -wA and w=2pi(F)

As it would not be equal to the 2pi (F)A so after doing this all, you will get the points of the slope, and then you can go for the ratio of wave speed and particle speed.