A marine navigational radar system emits electromagnetic pulses with a wavelength of 3.0\t… — JAMB UTME

A marine navigational radar system emits electromagnetic pulses with a wavelength of $3.0\text{ cm}$ . Given that the speed of electromagnetic waves in air is $3.0 \times 10^8\text{ m/s}$ , what is the frequency of the radar signal in gigahertz ( $\text{GHz}$ )?

Answer: 10 GHz

Answer

The frequency of the radar signal is

10\text{ GHz}

Converting

3.0\text{ cm}

to meters gives

\lambda = 0.03\text{ m}

. Using

f = c / \lambda

f = (3.0 \times 10^8\text{ m/s}) / 0.03\text{ m} = 1.0 \times 10^{10}\text{ Hz}

. Dividing by

10^9\text{ Hz/GHz}

yields

10\text{ GHz}

Step-by-Step Solution

Convert the given wavelength into fundamental SI units (meters).

\lambda = 3.0\text{ cm} = 3.0 \times 10^{-2}\text{ m}

The speed of light

c

is given in meters per second, so the wavelength must be expressed in meters to keep units consistent.

Rearrange the electromagnetic wave speed formula

c = f \lambda

to solve for frequency

f

f = \frac{c}{\lambda} = \frac{3.0 \times 10^8\text{ m/s}}{3.0 \times 10^{-2}\text{ m}} = 1.0 \times 10^{10}\text{ Hz}

Frequency is the ratio of wave propagation speed to wavelength.

Convert the frequency from hertz to gigahertz.

f = \frac{1.0 \times 10^{10}\text{ Hz}}{10^9\text{ Hz/GHz}} = 10\text{ GHz}

The question explicitly asks for the answer in gigahertz (

\text{GHz}

Key Concept

Electromagnetic wave propagation equation (

c = f \lambda

) and unit metric prefixes.

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Key Concept

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