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.

(a) The speed of propagation of the wave is

(b) (b) The velocity of a point on the string as a function of x and t is

The given parameters;

where;

(a) The speed of propagation of the wave is calculated as follows;

(b) The velocity of a point on the string as a function of x and t is calculated as follows;

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Answer with Explanation:

We are given that  the mathematical form of wave

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

In given mathematical form

k=Wave number

=Angular frequency

A=Amplitude

We know that

Speed of propagation of the wave=

b.Differentiate w.r.r t

The velocity of a point on the string as  a function of x and t is given  by