Question

Write an equation of the disturbance associated with a wave traveling along the x direction at t=8s if it's known to have an amplitude of 10 m, velocity of 4 m/s and a wavelength of 80 m

Answer 1

The equation of the disturbance associated with a wave traveling along the x direction at t=8s is y(x, 8) = 10 sin((2π/80)x - (2π/4)8).

Step-by-step explanation:

The equation of the disturbance associated with a wave traveling along the x direction at t=8s can be written as:

y(x, 8) = A sin(kx - wt)

Where A is the amplitude, k is the wave number, x is the position, w is the angular frequency, and t is the time.

Given that the amplitude is 10 m, the velocity is 4 m/s, and the wavelength is 80 m, you can use the formula:

w = 2πf = 2π/T = 2πv/λ

To find the angular frequency w. Then, use the formula:

k = 2π/λ

To find the wave number k. Substituting these values into the equation gives:

y(x, 8) = 10 sin((2π/80)x - (2π/4)8)