Question

A researcher measures the wavelength of an $\mathbf{1}\mathbf{.}\mathbf{20}\mathbf{-}\mathbf{GHz}$electromagnetic wave to be $\mathbf{0}\mathbf{.}\mathbf{500}\mathbf{}\mathbf{m}$. (a) Calculate the speed at which this wave propagates. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Short answer

a. The electromagnetic wave propagates at a speed of$6.00\times {10}^8\mathrm{m}/\mathrm{s}$

b. The speed of the electromagnetic wave is impossible.

c. The assumption about the combination of frequency and wavelength is inconsistent.

Step-by-step solution

Definition of Concept

Wavelength: The distance between identical points (adjacent crests) in adjacent cycles of a waveform signal propagated in space or along a wire is defined as the wavelength. This length is typically specified in wireless systems in meters (m), centimeters (cm), or millimeters (mm).

Find the speed at which this wave propagates

(a)

Considering the given information,

Frequency of the electromagnetic wave, $\mathrm{f}=1.20\mathrm{GHz}\left(\frac{{10}^9\mathrm{Hz}}{1\mathrm{GHz}}\right)=1.20\times {10}^9\mathrm{Hz}$

The wavelength of the electromagnetic wave,$\mathrm{\lambda }=0.500\mathrm{m}$

The relationship between the speed and wavelength of an electromagnetic wave,

$\mathrm{v}=\mathrm{f\lambda }$……………(1)

v denotes the electromagnetic wave's speed.

Substituting the values of frequency and wavelength in the above expression (1) we get,

$$\begin{gathered} \mathrm{v}=\left(1.20\times {10}^9\mathrm{Hz}\right)\left(0.500\mathrm{m}\right) \\ =6.00\times {10}^8\mathrm{m}/\mathrm{s} \end{gathered}$$

Therefore, the required electromagnetic wave propagates at a speed of$6.00\times {10}^8\mathrm{m}/\mathrm{s}$.

Find the unreasonable about this result

(b)

The computed electromagnetic wave speed is $6.00\times {10}^8\mathrm{m}/\mathrm{s}$, which is two times the

speed of light, which is impossible. As a result, the electromagnetic wave's speed is

excessive.

Therefore, the speed of the electromagnetic wave is impossible.

Find the assumptions are unreasonable or inconsistent

(c)

The wavelength or frequency value given is either too large or too short. As a result, the

the frequency-wavelength combination is illogical.

Therefore, the assumption about the combination of frequency and wavelength is inconsistent.