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In a certain experiment, a radio transmitter emits sinusoidal electromagnetic waves of frequency 110.0 MHz in opposite directions inside a narrow cavity with reflectors at both ends, causing a standing-wave pattern to occur. (a) How far apart are the nodal planes of the magnetic field? (b) If the standing-wave pattern is determined to be in its eighth harmonic, how long is the cavity?

Short Answer

Expert verified

A) l=1.36m B) x =10.92m

Step by step solution

01

STEP 1 To determine the wavelength of the waves

The electromagnetic wave travels with the speed of light and as the frequency f of the wave is related to the wavelength and the speed asc=Thus,λ=cf

02

Calculate the wavelength and the nodal planes

The frequency is given by f =110×106Hz The frequency of the electromagnetic waves doesn't change with changing the medium while the wavelength changes as the speed of the light changes by the medium. The wavelength is

λair=cf=3×108m/s110×106Hz=2.73m

The nodal planes of the magnetic field are apart with distance. Plug the values for to get l

l=λ2=2.732=1.36m

Therefore,λair=2.73m

03

Calculate the distance between adjacent nodal planes

For eight antinodes planes of the electric field, use equationx=82λ to get the distance between adjacent nodal planes x which represents the length of the cavity. Substitute the values we have,

x=82(2.73m)=10.92m

Therefore, the distance between adjacent nodal planes x is 10.92m

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