A radio transmitter emits electromagnetic waves with a frequency of 1.0 \times 10^8\text{ … — JAMB UTME

A radio transmitter emits electromagnetic waves with a frequency of $1.0 \times 10^8\text{ Hz}$ . Given that the speed of light in a vacuum is $c = 3.0 \times 10^8\text{ m s}^{-1}$ , what is the wavelength of the emitted wave?

$3.0\text{ m}$ Answer
B
$3.0 \times 10^{16}\text{ m}$
C
$0.33\text{ m}$
D
$3.0 \times 10^{-1}\text{ m}$

Answer

The wavelength of the emitted radio wave is

3.0\text{ m}

According to the wave equation

c = f \lambda

, the wavelength is found by dividing the speed of light by frequency:

\lambda = \frac{3.0 \times 10^8\text{ m s}^{-1}}{1.0 \times 10^8\text{ Hz}} = 3.0\text{ m}

Step-by-Step Solution

Identify the given parameters and fundamental formula

Speed of light

c = 3.0 \times 10^8\text{ m s}^{-1}

and frequency

f = 1.0 \times 10^8\text{ Hz}

. The electromagnetic wave relation is

c = f \lambda

All electromagnetic waves travel at the speed of light in a vacuum.

Rearrange the formula to solve for wavelength

\lambda = \frac{c}{f}

Dividing both sides of the wave equation by frequency isolates wavelength.

Substitute values into the equation and compute the result

\lambda = \frac{3.0 \times 10^8}{1.0 \times 10^8} = 3.0\text{ m}

Performing the division yields the correct wavelength.

Key Concept

Relationship between wave speed, frequency, and wavelength for electromagnetic radiation in a vacuum.

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