Answer:
Speed, [tex]v=1.86\times 10^8\ m/s[/tex]
Explanation:
It is given that,
A light wave is described by the following function as :
[tex]E(x,t)=A\ cos[(1.57\times 10^7)x-(2.93\times 10^{15})t][/tex].....(1)
The general equation of wave is given by :
[tex]E=Acos(kx-\omega t)[/tex]........(2)
On comparing equation (1) and (2)
[tex]k=(1.57\times 10^7)[/tex]
[tex]\dfrac{2\pi}{\lambda}=(1.57\times 10^7)[/tex]
[tex]\lambda=\dfrac{2\pi}{(1.57\times 10^7)}[/tex]
Wavelength, [tex]\lambda=4.002\times 10^{-7}\ m[/tex]
[tex]\omega=(2.93\times 10^{15})[/tex]
[tex]\dfrac{2\pi}{T}=(2.93\times 10^{15})[/tex]
[tex]\dfrac{1}{T}=\dfrac{(2.93\times 10^{15})}{2\pi}[/tex]
Frequency, [tex]f=4.66\times 10^{14}\ Hz[/tex]
Let v is the speed of the light wave. It is given by :
[tex]v=f\times \lambda[/tex]
[tex]v=4.66\times 10^{14}\ Hz\times 4.002\times 10^{-7}\ m[/tex]
[tex]v=1.86\times 10^8\ m/s[/tex]
So, the speed of the light wave is [tex]1.86\times 10^8\ m/s[/tex]. Hence, this is the required solution.
