Question

A harmonic wave moving in the positive x direction has an amplitude of 3.7 cm, a speed of 42.0 cm/s, and a wavelength of 42.0 cm. Assume that the displacement is zero at x = 0 and t = 0.

Calculate the displacement due to the wave at x = 10.0 cm, t = 20.0 s.

Answer 1

Equation for a Harmonic Wave is y = A Sin(kx-Wt+P), P is phase

Given A=3.7 cm

k=2*pi/42

v = 42cm/s = W/k , so, W = k*v = 2*pi

Given displacement is zero at x = 0 and t = 0 so, P =0

So,

y = A Sin(kx-Wt)

At x = 10.0 cm, t = 20.0 s,

y = 3.7 sin((2*pi/42)*10- 2*pi*20)

y = 3.7 sin((20pi/42)-40pi)

y = - 3.06 cm