Question

What is the frequency of radio waves transmitted by a station? If the wavelength of these waves is $300\,m$. The Speed of radio waves is \[3 \times {10^8}\,m{s^{ - 1}}\].

Answer 1

Hint: A radio station transmits radio waves at a particular frequency. The velocity of any wave is equal to the product of its wavelength and frequency. Use this relation to calculate the frequency of the given radio waves.

Complete step by step answer:
It is given that the speed of radio waves, $v = 3 \times {10^8}\,m{s^{ - 1}}$. The wavelength of radio waves, $\lambda = 300\,m$. It is required to find the frequency $\left( f \right)$ of radio waves.We know that the velocity of any wave,
$v = \lambda \times f$
$ \Rightarrow f = \dfrac{v}{\lambda }$
Substitute the value of velocity and wavelength in the above formula, we got
$ \Rightarrow f = \dfrac{{3 \times {{10}^8}}}{{300}}{s^{ - 1}}$
Further calculating
$ \Rightarrow f = {10^6}{s^{ - 1}}$
$\therefore f = 1\,MHz$

Hence, the frequency of the given radio waves is $1\,MHz$.

Additional information:In 1867, James Clerk Maxwell, a Scottish physicist, was the first person who predicted radio waves by mathematical work. His mathematical theory is now known as Maxwell’s equations. He predicted that a combination of electric and magnetic fields travel through space as an electromagnetic wave.

He proposed that the light consists of electromagnetic waves of very short wavelength.The range of frequencies of radio waves are from $30\,Hz$ to $300\,GHz$. Radio waves are used in standard broadcast radio and television, navigation and air-traffic control, cellular telephony, and remote-controlled toys etc.

Note: Radio waves travel with the speed of light because these are the electromagnetic waves. All the electromagnetic waves travel at the speed of light. In free space the speed of light is constant and it is $c = 3 \times {10^8}\,m{s^{ - 1}}$. The velocity of light travelling in the medium of refractive index $\mu $ is $v = \dfrac{c}{\mu }$.