Question

The wave function (in S.I. units) for an electromagnetic wave is given as-
$\psi (x,t)={10}^3\sin \pi (3\times {10}^{6}x-9\times {10}^{14}t)$ The speed of the wave is:

• A. $9\times {10}^{14}m/s$
• B. $3\times {10}^{8}m/s$
• C. $3\times {10}^{6}m/s$
• D. $3\times {10}^{7}m/s$

Answer 1

The correct option is B $3\times {10}^{8}m/s$

Given: The wave function (in S.I. units) for an electromagnetic wave is given as- $\psi (x,t)={10}^3\sin \pi (3\times {10}^{6}x-9\times {10}^{14}t)$

To find the speed of the wave

Solution:

We know electromagnetic wave eqution is

$E=E_0\cos (kz-\omega t)$

And given equation is

$\psi (x,t)={10}^3\sin \pi (3\times {10}^{6}x-9\times {10}^{14}t)$

By comparing these two, we get

$\omega =9\times {10}^{14}$ and

$k=3\times {10}^6$

we also know,

Speed of electromagnetic wave, $v=\frac{\omega }{k}$

where v is the speed of the light

Hence, $v=\frac{9\times {10}^{14}}{3\times {10}^6}⟹v=3\times {10}^{8}m/s$

is the speed of the wave