Question

For an electromagnetic wave given by. \( \vec{E}=E_{0} \sin \left(4 \times 10^{10} \pi t-k x\right) \hat{k} \). wavelength of electromagnetic wave in vacuum, is

Answer 1

Given 

\(\vec E = E_0sin (4\times 10^{10} \pi t - kx)\hat k\)

\(\lambda = ?\)

we know that speed of electromagnetic in vaccum is 3 x 10⁸ m/s

\(\vec E = E_0sin (4 \times 10^{10}\pi t - kx)\)

\(w = 4 \times 10^{10} \pi\)

\(2\pi f = 4 \times 10^{10} \pi\)

\(f = 2\times 10^{10} Hz\)

wavelength 

\(\lambda = \frac vf\)

\(\lambda = \frac{3\times 10^8}{2\times 10^{10}}\)

\(\lambda = 1.5 \times 10^{-2} m\)

\(\lambda = 1.5 cm\)