Problem: The equation of a transverse wave traveling along a very long string is y = 5.43 sin(0.0246πx+ 8.65πt), where x and y are expressed in centimeters and t is in seconds. Determine(a) the speed, (b) the direction of propagation of the wave and (c) the maximum transverse speed of a particle in the string. (d) What is the transverse displacement at x = 1.77 cm when t = 0.705 s?

FREE Expert Solution

The general equation of a transverse wave is:

$\overline{){\mathbf{y}}{\mathbf{=}}{\mathbf{A}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\left(}}{\mathbf{k}}{\mathbf{x}}{\mathbf{+}}{\mathbf{\omega }}{\mathbf{t}}{\mathbf{\right)}}}$

Speed of the wave:

$\overline{){\mathbf{v}}{\mathbf{=}}\frac{\mathbf{\omega }}{\mathbf{k}}}$

(a)

Speed, v =  ω/k = 8.65π/0.0246π = 351.6 m/s.

The speed of the wave is 351.6 m/s.

Problem Details

The equation of a transverse wave traveling along a very long string is y = 5.43 sin(0.0246πx+ 8.65πt), where x and y are expressed in centimeters and t is in seconds. Determine

(a) the speed, (b) the direction of propagation of the wave and (c) the maximum transverse speed of a particle in the string. (d) What is the transverse displacement at x = 1.77 cm when t = 0.705 s?