An FM radio station transmits electromagnetic waves at a frequency of 1.0 \times 10^8\text… — JAMB UTME

An FM radio station transmits electromagnetic waves at a frequency of $1.0 \times 10^8\text{ Hz}$ in a vacuum. Given that the speed of light in a vacuum is $3.0 \times 10^8\text{ m/s}$ , what is the wavelength of these radio waves in meters?

Answer: 3 m

Answer

The wavelength of the radio waves is

3.0\text{ m}

Applying the wave equation

c = f\lambda

, rearranging to

\lambda = \frac{c}{f}

, and substituting

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

and

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

gives a wavelength of

3.0\text{ m}

Step-by-Step Solution

Identify given parameters and key formula

Speed of light

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

, frequency

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

, wave equation

c = f\lambda

The electromagnetic wave equation relates speed, frequency, and wavelength.

Rearrange for wavelength and substitute given values

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

Dividing the speed of propagation by the wave frequency yields the spatial wavelength.

Key Concept

Wave equation relating speed, frequency, and wavelength of electromagnetic waves

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