The Poynting vector of an electromagnetic wave in vacuum is:

S = {(120 W/m2) sin2[(8.0 rad/m) z + (6.28 × 109 rad/s) t]} k
What is the frequency of the wave?

Question

Question

Answer 1

Concept:

Poynting vector represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field.
The SI unit of the Poynting vector is the watt per square meter(w/m²).
It is named after its discovery John Henry Poynting who first derived it in 1884.

The general expression of a wave propagating in the z-direction is given by:

\(P\left( {z,t} \right) = {P_{max}}\cos \left( {kz - ω t + \phi } \right)\)

k = wave number

ω = frequency (in rad)

Calculation:

Given Poynting vector of an electromagnetic wave in a vacuum:

S = {(120 W/m2) sin2[(8.0 rad/m) z + (6.28 × 109 rad/s) t]} k

Comparing this with the general expression, the angular frequency of the wave will be:

\(ω= 2\pi f\)

Here angular frequency(ω) is equal to 6.28×10⁹rad/s.

\(f=\frac{ω}{2\pi}\)

\(f=\frac{6.28 \times10^{9}}{2\times 3.14}\)

\(f=\frac{2 \times10^{9}}{2}\)

\(f=10^{9}=1000\times 10^{6} \)

Since 1 MHz = 10⁶ Hz

f = 1000 MHz

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