Question

A radio station is transmitting its signals at a frequency of $400 MHz$.If the velocity of radio waves is \[3 \times {10^8}m/s\], calculate the wavelength of radio waves.

Answer 1

Hint:The radio waves are being transmitted at a particular frequency. These radio waves are travelling with the speed of light. The velocity of the radio waves is the frequency times the wavelength of the waves. By using this relation, the wavelength of radio waves of radio waves can be calculated.

Formula Used:
The frequency of radio waves is: \[f = \dfrac{c}{\lambda }\]
where, \[f\] is the frequency of the wave, \[c\] is the speed of the wave and \[\lambda \] is the wavelength of the wave.

Complete step by step answer:
 The signals transmitted from the radio station have a particular frequency and velocity. These signals are radio waves. Radio waves are a part of the electromagnetic spectrum. Every wave of the electromagnetic spectrum has a particular frequency. This particular frequency corresponds to a particular wavelength of the wave. This relation can be described as follows:
\[f = \dfrac{c}{\lambda }\]
This formula can also be written in terms of wavelength.
\[\lambda = \dfrac{c}{f}\] \[ \to (1)\]
The frequency of the signal or radio waves is given as 400 MHz and the velocity is \[3 \times {10^8}m/s\]. Therefore, \[f = 440MHz\] and \[c = 3 \times {10^8}m/s\]. Substituting in equation (1).
\[\lambda = \dfrac{c}{f} \\
\Rightarrow\lambda = \dfrac{{3 \times {{10}^8}m/s}}{{440MHz}} \\
\Rightarrow\lambda = \dfrac{{3 \times {{10}^8}m/s}}{{440 \times {{10}^6}Hz}} \\
\Rightarrow\lambda = 0.0068 \times {10^2}m \\
\therefore\lambda = 0.68m\]

Therefore, the wavelength of radio waves is 0.68 metre.

Note:The radio waves are travelling with the speed of light. This is because radio waves are a part of the electromagnetic spectrum. All the waves of the electromagnetic spectrum travel with the speed of light. So the formula of equation (1) is \[\lambda = \dfrac{c}{f}\] where \[c\] is the speed of light. But, some waves which are not part of the electromagnetic spectrum have different velocities of light. Therefore, wavelengths for them can be written as \[\lambda = \dfrac{v}{f}\], where \[v\] is the velocity of the given wave.