Waves on a String Video Lessons

Concept

# Problem: The equation y(x,t)=Acos2πf(xv−t) may be written as y(x,t)=Acos[2πλ(x−vt)].a. 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.b. 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.

###### FREE Expert Solution

a. Transverse wave:

$\overline{){\mathbf{y}}{\mathbf{\left(}}{\mathbf{x}}{\mathbf{,}}{\mathbf{t}}{\mathbf{\right)}}{\mathbf{=}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\left[}}\frac{\mathbf{2}\mathbf{\pi }}{\mathbf{\lambda }}{\mathbf{\left(}}{\mathbf{x}}{\mathbf{-}}{\mathbf{v}}{\mathbf{t}}{\mathbf{\right)}}{\mathbf{\right]}}}$

Velocity, v = dy/dt

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###### Problem Details

The equation y(x,t)=Acos2πf(xv−t) may be written as y(x,t)=Acos[2πλ(x−vt)].

a. 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.

b. 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.