Answer to Question #159650 in Physics for Hilario Encarnacion

Question

A sinusoidal wave travelling in the positive x direction has an amllplitude of 15.0 cm, a wavelength of 40.0 cm, and a frequency pf 8.00 Hz. The vertical position of an element of the medium at t=0 and x =0 is also 15.0 cm.

A. Find the wave number k, period T, angular frequency w, and speed v of the wave

B. Write a general expression for the wave function

Answer 1

Let's denote: $A = 15cm =0.15m$ is the amplitude, $\lambda = 40cm = 0.4m$ is the wavelength, $f = 8Hz$ is the frequency.

The wave number is given as:

$$k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{0.4} = 5\pi\space m^{-1}$$

The angular frequency is:

$$\omega = 2\pi f = 16\pi \space rad/s$$

The speed is:

$$v = \lambda f = 3.2m/s$$

The general expression for the wave is:

$$y(x,t) = A\cos(kx - \omega t)\\ y(x,t) = 0.15\cos(5\pi x - 16\pi t)\space [m]$$

Answer. A) $k = 5\pi \space m^{-1}, \omega = 16\pi \space rad/s, v = 3.2m/s$, B) $y(x,t) = 0.15\cos(5\pi x - 16\pi t)\space [m]$.