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) t…

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asked Sep 15, 2021 219k views

1 Answer

Yuefengz · Answer 1 · 2021-09-20T22:36:09+0000

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.