Question

The electric field component of an electromagnetic wave is described by

Eₓ(z,t)=400N/C ​sin((1.083×10⁷)z−(3.25×10¹⁵)t). What is the wavelength of this wave?

Answer 1

The wavelength λ of the electromagnetic wave given by the equation is approximately 0.58 meters.

Step-by-step explanation:

The equation given is for an electromagnetic wave with electric field component E₀(z,t) = 400N/C ​sin((1.083×10⁷)z−(3.25×10¹⁵)t). To find the wavelength, we look at the term within the sine function that multiplies the spatial coordinate z. This term is related to the wavenumber k, which is 1.083×10⁷ rad/m. The wavenumber is related to wavelength λ by k = 2π/λ. Solving for λ gives us λ = 2π/k = 2π/(1.083×10⁷ rad/m). Calculating this, we obtain a wavelength of approximately 0.58 meters.

The wavelength of an electromagnetic wave can be determined by the equation:

wavelength = 2π / k

where k is the wavenumber. In this case, k = 1.083 × 10^7 m^-1. Plugging this value into the equation gives:

wavelength = 2π / (1.083 × 10^7)

Calculating this gives:

wavelength ≈ 5.8 × 10^-7 m

So, the wavelength of this wave is approximately 5.8 × 10^-7 meters.