Question

Some radar systems detect the size and shape of objects such as aircraft and geological terrain. Approximately what is the smallest observable detail utilizing\(500{\rm{ }}MHz\)radar?

Short answer

The smallest detail observable is \(0.6{\rm{ }}m\).

Step-by-step solution

Definition of frequency

Frequency is the number of waves that pass through a specific spot in a specific length of time.

Given information and Formula to be used

The frequency of radar is: \(\begin{array}{c}f = 500MHz\\ = 5 \times {10^8}\;Hz\end{array}\)

The speed of light value is: \(c = 3 \times {10^8}\;m/s\)

For an electromagnetic wave, the relationship between propagation speed, wavelength, and frequency is given by,

\(c = f\lambda \)

Calculate the wavelength

Consider the given values and simplify,

\(\begin{array}{c}c = f\lambda \\3 \times {10^8} = 5 \times {10^8} \times \lambda \\\lambda = 0.6{\rm{ }}m\end{array}\)

Therefore, the wavelength is \(0.6{\rm{ }}m\).