Question

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

Answer 1

Hint: 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.