Question

An electromagnetic wave has an electric field given by

Answer 1

Answer:

λ = 157 μm

Explanation:

given,

$\vec{E}(y,t)=[ 3.9\times 10^5\ V/m cos(ky-(1.20\times 10^{13}\ rad/s )t)]\vec{k}$

now,

ω = 1.2 x 10¹³ rad/s

$f =\dfrac{\omega}{2\pi}$

$f =\dfrac{1.2\times 10^{13}}{2\pi}$

f = 1.91 x 10¹² Hz

determine the wavelength of the E M wave

 $\lambda = \dfrac{c}{f}$

 $\lambda = \dfrac{3\times 10^8}{1.91\times 10^{12}}$

   λ = 1.57 x 10⁻⁴ m

   λ = 157 x 10⁻⁶ m

   λ = 157 μm

hence, the wavelength of the wave is equal to λ = 157 μm