A standing electromagnetic wave in a certain material has frequency $2.20\times {10}^{10}\mathrm{Hz}$. The nodal planes of $\overrightarrow{B}$are 4.65 mm apart. Find the speed of propagation of the wave.

The standing EM wave

The EM waves can form standing waves when EM waves are reflected from the end of a transmission line.

The wavelength of standing wave produced due to two nodal planes

The wavelength of standing wave is produced due to two nodal planes is given by

$x=\frac{\lambda }{2}$

Where, x is the distance between two nodal planes and $\lambda$is the wavelength of wave.

The speed of propagating wave

The speed of propagating wave is given by

$\mathrm{v}=\mathrm{f\lambda }$

Where, v is the speed of propagation of wave and f is the frequency of wave.

Given: $\mathrm{x}=4.65\mathrm{mm}$,$\mathrm{f}=2.20\times {10}^{10}\mathrm{Hz}$

Using

$x=\frac{\lambda }{2}$

Put the value of x in above equation

$$\begin{gathered} 4.65\mathrm{mm}=\frac{\mathrm{\lambda }}{2} \\ \mathrm{\lambda }=2(4.65) \\ \mathrm{\lambda }=9.3\mathrm{mm} \end{gathered}$$

Thus, the value of wavelength of wave is $\mathrm{\lambda }=9.3\mathrm{mm}$

Using

$v=f\lambda$

Now put the value of constants in above equation

$$\begin{gathered} \mathrm{v}=\mathrm{f\lambda } \\ \mathrm{v}=2.20\times {10}^{10}\mathrm{Hz}\times 9.3\times {10}^{-3}\mathrm{m} \\ \mathrm{v}=2.05\times {10}^8\mathrm{m}/\mathrm{s} \end{gathered}$$

Thus, the speed of propagation of the wave is $\mathrm{v}=2.05\times {10}^8\mathrm{m}/\mathrm{s}$.