Question

A sinusoidal wave on a string travelling in the +x direction has wave number
3/m and angular frequency 20 rad/s. If the amplitude is 0.2m and the point
at x = 0 is at its maximum displacement and t = 0, find the equation of the
wave.

Answer 1

Answer:

∴ y = 0.2 cos(3x − 20t)

Explanation:

Given,

A sinusoidal wave on a string travelling in the +x direction has wave number

3/m and angular frequency 20 rad/s.

The amplitude is 0.2m and the point  at x = 0 is at its maximum displacement and t = 0

To find: the equation of the wave.

Solution:

Let y = A sin(kx − ωt + φ)

At x = 0, t = 0, the wave has the maximum displacement and y = A:

A = A sin(0 − 0 + φ)

or sin φ = 1 → φ = π/2

∴ y = A sin(kx − ωt + π/2) = A cos(kx − ωt)

∴ y = 0.2 cos(3x − 20t)