A transverse harmonic wave on a string is described by $y(x,t) = 3.0 \sin(36t + 0.018x + \pi/4)$ whe

Question

A transverse harmonic wave on a string is described by $y(x,t) = 3.0 \sin(36t + 0.018x + \pi/4)$ where $x$ and $y$ are in cm and $t$ is in seconds. What are the speed and direction of its propagation?

Professor PC Thomas Classes · Answer

The argument is in the form $(\omega t + kx)$, indicating propagation in the negative x-direction. Speed $v = \omega / k = 36 / 0.018 = 2000$ cm/s = 20 m/s.