A satellite communication system transmits an ultra-high frequency electromagnetic wave wi… — JAMB UTME

A satellite communication system transmits an ultra-high frequency electromagnetic wave with a wavelength of $0.05\text{ m}$ . If the wave travels at a speed of $3.0 \times 10^{8}\text{ m/s}$ in a vacuum, what is the frequency of the transmission in gigahertz ( $\text{GHz}$ )?

Answer: 6 GHz

Answer

The frequency of the electromagnetic transmission is

6\text{ GHz}

Using the wave equation

c = f \lambda

, the frequency is

f = \frac{c}{\lambda} = \frac{3.0 \times 10^8\text{ m/s}}{0.05\text{ m}} = 6.0 \times 10^9\text{ Hz}

. Converting to gigahertz (

1\text{ GHz} = 10^9\text{ Hz}

) yields

6\text{ GHz}

Step-by-Step Solution

Identify the relationship between electromagnetic wave velocity, frequency, and wavelength.

c = f \lambda

, where

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

and

\lambda = 0.05\text{ m}

All electromagnetic waves travel at the speed of light

c

in a vacuum.

Rearrange the wave equation to isolate frequency (

f

f = \frac{c}{\lambda} = \frac{3.0 \times 10^8\text{ m/s}}{0.05\text{ m}} = 6.0 \times 10^9\text{ Hz}

Dividing the wave speed by the wavelength yields the frequency in hertz.

Convert the frequency into gigahertz (

\text{GHz}

\frac{6.0 \times 10^9\text{ Hz}}{10^9\text{ Hz/GHz}} = 6\text{ GHz}

The prefix giga (G) denotes a factor of

10^9

Key Concept

Electromagnetic wave propagation equation (

c = f \lambda

) and unit conversion

Estimated Time:1m 15s

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