Question

A plane electromagnetic wave propagating in $x(-)$ direction as a wave function (in SI units) is given as
$\Phi (x,t)={10}^3\sin \pi (3\times {10}^{6}x-9\times {10}^{14}t)$
The speed of the wave is

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

Answer 1

Answer: (C)

$3\times {10}^{8}m/s$

Comparing the given equation of wave with
$y=a\sin (\frac{2\pi }{\lambda }x-\frac{2\pi }{T}t)$ we have
$\frac{2\pi }{\lambda }=\pi \times 3\times {10}^6$
or $\lambda =\frac{2}{3\times {10}^6}m$
and $\frac{2\lambda }{T}=\pi \times 9\times {10}^{14}$
or $v=\frac{1}{T}=\frac{9}{2}\times {10}^{14}Hz$
$\therefore$ Speed of wave,
$c=v\lambda =\frac{(9\times {10}^{14})}{2}\times \frac{2}{(3\times {10}^6)}$
$=3\times {10}^{8}m/s$.