The equation y(x, t)=acos2πf(xv−t) may be written as y(x, t)=acos[2πλ(x−vt)].

use the last expression for y(x, t) to find an expression for the transverse velocity vy of a particle in the string on which the wave travels. express your answer in terms of the variables a, v, λ, x, t, and appropriate constants.

find the maximum speed of a particle of the string. express your answer in terms of the variables a, v, λ, x, t, and appropriate constants.

v=2πf A sin 2πf(xv−t)

Vmax= 2πf A

Explanation:

Given that

The wave equation

y(x,t)=Acos[2πλ(x−vt)]

y(x,t)=Acos2πf(xv−t)

As we know that rate of change in the displacement is known as velocity.

y(x,t)=Acos[2πλ(x−vt)]

y(x,t)=Acos2πf(xv−t)

In the above equation all other quantity is constant when we differentiate with respect to time t

v=2πf A sin 2πf(xv−t)

The maximum speed will be when sin 2πf(xv−t)  become unit.

Therefore maximum speed is 2πf A.

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