Question

Wave motion is characterized by two velocities: the velocity with which the wave moves in the medium (e.g., air or a string) and the velocity of the medium (the air or the string itself). Consider a transverse wave traveling in a string. The mathematical form of the wave is y(x,t)=Asin(kx−ωt). a. Find the speed of propagation vp of this wave.b. Find the y velocity vy(x,t) of a point on the string as a function of x and t.

Answer 1

Answer with Explanation:

We are given that  the mathematical form of wave

$y(x,t)=Asin(kx-\omega t)$

a.We have to find the speed of propagation of this wave

In given mathematical form

k=Wave number

$\omega$=Angular frequency

A=Amplitude

We know that

Speed of propagation of the wave=$v_p=\frac{\omega}{k}$

b.Differentiate w.r.r t

$v_y(x,t)=-A\omega cos(kx-\omega t)$

The velocity $v_y(x,t)$ of a point on the string as  a function of x and t is given  by

$v_y(x,t)=-A\omega cos(kx-\omega t)$