An electromagnetic standing wave in air has frequency 75.0 MHz. What is the distance between a nodal plane of Eand the closest nodal plane of B?

Short Answer

Expert verified

The distance between a nodal plane of Eand the closest nodal plane of Bis 1m.

Step by step solution

01

Step 1: 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 a nodal plane of Eand nodal plane ofB

The wavelength of standing wave is produced due to a nodal plane of Eand nodal plane of Bis given by

role="math" localid="1664426475142" x=λ4

Where, xis the distance between two nodal planes and λis the wavelength of wave.

Speed of propagating wave

The speed of propagating wave is given by

v=

Where, vis the speed of propagation of wave and role="math" localid="1664426617586" fis the frequency of wave.

02

The calculation of wavelength of wave

Given: f=75MHz=75×106Hz,v=3×108m/s,

Using

v=

Put the values of constants in above equation

3×108ms-1=75×106Hz×λλ=3×10875×106λ=4m

Thus, the wavelength of wave is 4m

03

The calculation of nodal plane of E→ and closest nodal plane of  B→

Using

x=λ4

Now, put the value of wavelength in above equation

x=4m4x=1m

Thus, the distance between a nodal plane of Eand the closest nodal plane oflocalid="1664427274713" Bis localid="1664427133460" 1m.

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