Question

What is the wavelength of the microwaves of frequency $2 \times {10^9}Hz$ ?

Answer 1

Electromagnetic waves are of different types like microwaves, radio waves, infra-red waves and ultraviolet waves. Microwaves are the waves that have a high frequency in the electromagnetic waves. The wavelength can be calculated from the frequency and velocity of light by substituting the values in the below formula.
$\lambda = \dfrac{c}{\nu }$
$\lambda$ is wavelength in metres
$c$ is velocity of light in metres per second
$\nu$ is frequency in hertz.

Complete Step By Step Answer:
Various electromagnetic waves can be observed from the electromagnetic spectrum. Different types of electromagnetic waves include microwaves, radio waves, infra-red waves and ultraviolet waves.
Microwaves are the part of an electromagnetic radiation with a range of wavelengths from one metre to one millimetre. The frequency ranges from $1GHz$ to $1000GHz$ .
Microwaves can be produced by special vacuum tubes and magnetrons.
Given that the microwave has a frequency of $2 \times {10^9}Hz$
The velocity of light must be taken in metres per second only which is equal to $3 \times {10^8}m{\sec ^{ - 1}}$
Substitute these both values in the above formula, to obtain the value of wavelength.
$\lambda = \dfrac{{3 \times {{10}^8}m{{\sec }^{ - 1}}}}{{2 \times {{10}^9}Hz}}$
By simplifying the above fraction, the value of wavelength will be $\lambda = 0.15m$
Thus, the wavelength of the microwaves of frequency $2 \times {10^9}Hz$ is $0.15m$ .

Note:
Generally, the frequency can be written in the units of hertz but hertz is defined as one cycle per second which means hertz is nothing but the inverse of a second. Thus, in the above fraction, the units of ${\sec ^{ - 1}}$ were cancelled and the units of metres remained which were the units of wavelength.