Question

A wave traveling in a string in the positive x direction has a wavelength of 35 cm, an amplitude of 8.4 cm, and a period of 1.2 s. What is the wave equation (in base SI units) that correctly describes this wave

Answer 1

Explanation:

It is given that,

Wavelength of a wave, $\lambda=35\ cm=0.35\ m$

Amplitude, $A=8.4\ cm$

Period of the wavelength, t = 1.2 s

The wave is traveling in a string in the positive x direction. We need to write the wave equation for this conditions.

The general equation of the wave when it is traveling in +x direction is given by :

$y=A\sin(kx-\omega t)$

A is amplitude

k is propagation constant

$k=\dfrac{2\pi}{\lambda}\\\\k=\dfrac{2\pi}{0.35}\\\\k=17.95\ m^{-1}\approx 18\ m^{-1}$

$\omega$ is angular frequency

$\omega=\dfrac{2\pi}{T}\\\\\omega=\dfrac{2\pi}{1.2}\\\\\omega=5.23\ s^{-1}$

So, the wave equation is given by :

$y(x,t)=(0.084) \sin (18 x - 5.2 t)$

Hence, this is the required solution.