An electromagnetic microwave signal used in telecommunication has a wavelength of 0.02\tex… — JAMB UTME

An electromagnetic microwave signal used in telecommunication has a wavelength of $0.02\text{ m}$ in a vacuum. Given that the speed of light in a vacuum is $3.0 \times 10^8\text{ m/s}$ , calculate the frequency of the signal in gigahertz ( $\text{GHz}$ ).

Answer: 15 GHz

Answer

The frequency of the microwave signal is

15\text{ GHz}

Using the electromagnetic wave equation

c = f \lambda

, the frequency in Hz is calculated as

f = \frac{c}{\lambda} = \frac{3.0 \times 10^8\text{ m/s}}{0.02\text{ m}} = 1.5 \times 10^{10}\text{ Hz}

. Dividing by

10^9

to convert into gigahertz gives

15\text{ GHz}

Step-by-Step Solution

Identify the given parameters and formula.

Speed of light

c = 3.0 \times 10^8\text{ m/s}

, wavelength

\lambda = 0.02\text{ m}

, and wave equation

c = f \lambda

Electromagnetic waves propagate at speed

c

in a vacuum, relating frequency and wavelength.

Calculate the frequency in Hertz (Hz).

f = \frac{3.0 \times 10^8}{0.02} = 1.5 \times 10^{10}\text{ Hz}

Dividing the wave speed by the wavelength yields the frequency.

Convert the unit from Hz to GHz.

\frac{1.5 \times 10^{10}\text{ Hz}}{10^9\text{ Hz/GHz}} = 15\text{ GHz}

One gigahertz (

1\text{ GHz}

) equals

10^9\text{ Hz}

Key Concept

Relationship between speed of light, frequency, and wavelength (

c = f \lambda

) for electromagnetic radiation.

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