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

Step-by-step 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=(2\pi)/(\lambda)\\\\k=(2\pi)/(0.35)\\\\k=17.95\ m^(-1)\approx 18\ m^(-1)`

`\omega` is angular frequency

`\omega=(2\pi)/(T)\\\\\omega=(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.