Question

Given the wave function: Y(x,t) = 5sin27(0.2x - 3t); (x = meters, t = sec.): What are the amplitude, frequency, wavelength, angular frequency and phase velocity of the wave? In which direction is it traveling? (Note: this wave is not a light wave traveling in a vacuum so va = 3 x 108 is not valid)

Answer 1

Answer:

$A=5 m, \omega=81s^{-1}, f=12.89s^{-1}, \lambda=1.16m, v=4.95\frac{m}{s}$ and the wave is traveling in the positive x-direction, since we have a wave function like this, $y(x,t) = A sin(kx - \omega t)$

Explanation:

A transverse harmonic wave traveling in the x axis is defined by:

$y(x,t) = A sin(kx \pm \omega t \pm \phi)(1)$

Where A is the amplitude, k the wave number. $\omega$ the angular frequency, $\phi$ the phase constant and the $\pm$ of the term $\omega t$ gives us the direction of propagation

Recall that $\lambda=\frac{2\pi}{k}, f=\frac{\omega}{2\pi}$ and $v=\lambda f$

Where  $\lambda$ is the wavelength, $f$ the frequency and $v$ the phase velocity.

We have:

$Y(x,t) = 5sin27(0.2x - 3t)\\Y(x,t) = 5sin(5.4x - 81t)$

So, you can relate our wave function with the general wave function(1):

$\phi=0\\A=5 m\\k=5.4m^{-1}\\ \omega=81s^{-1}\\ f=\frac{81s^{-1}}{2\pi}=12.89s^{-1}\\ \lambda=\frac{2\pi}{5.4m^{-1}}=1.16m\\v=(1.16m)(12.89s^{-1})=14.95\frac{m}{s}$

The wave is traveling in the positive x-direction, since we have a wave function like this, $y(x,t) = A sin(kx - \omega t)$