Question

As it travels through a crystal, a light wave is described by the function E(x,t)=Acos[(1.57×107)x−(2.93×1015)t]. In this expression, x is measured in meters and t is measured in seconds.
Part A
What is the speed of the light wave?
Express your answer to three significant figures and include appropriate units.

Answer 1

Answer:

Speed, $v=1.86\times 10^8\ m/s$

Explanation:

It is given that,

A light wave is described by the following function as :

$E(x,t)=A\ cos[(1.57\times 10^7)x-(2.93\times 10^{15})t]$.....(1)

The general equation of wave is given by :

$E=Acos(kx-\omega t)$........(2)

On comparing equation (1) and (2)

$k=(1.57\times 10^7)$

$\dfrac{2\pi}{\lambda}=(1.57\times 10^7)$

$\lambda=\dfrac{2\pi}{(1.57\times 10^7)}$

Wavelength, $\lambda=4.002\times 10^{-7}\ m$

$\omega=(2.93\times 10^{15})$

$\dfrac{2\pi}{T}=(2.93\times 10^{15})$

$\dfrac{1}{T}=\dfrac{(2.93\times 10^{15})}{2\pi}$

Frequency, $f=4.66\times 10^{14}\ Hz$

Let v is the speed of the light wave. It is given by :

$v=f\times \lambda$

$v=4.66\times 10^{14}\ Hz\times 4.002\times 10^{-7}\ m$

$v=1.86\times 10^8\ m/s$

So, the speed of the light wave is $1.86\times 10^8\ m/s$. Hence, this is the required solution.