Question

The wavelength (in $SI$ units) for an electromagnetic wave is given as $\psi(x, t)=10^{3} \sin \pi\left(3 \times 10^{6} x-9 \times 10^{14} t\right)$ The speed of the wave is $y \times 10^{7} m / s$. Find $y$.

Answer 1

$\Psi(x, t)=10^{3} \sin \pi\left(3 \times 10^{6} x-9 \times 10^{14} t\right)$
$\Psi(x, t)=10^{3} \sin \left(3 \pi \times 10^{6} x-9 \pi \times 10^{14} t\right)$
speed $=v=\frac{\omega}{k}=\frac{9 \pi \times 10^{14}}{3 \pi \times 10^{6}}$
$=3 \times 10^{8} \,m / s$