Question

The frequency of radio waves corresponding to a wavelength of \[10m\] is
(A) \[3\times {{10}^{7}}Hz\]
(B) \[3.3\times {{10}^{8}}Hz\]
(C) \[3\times {{10}^{9}}Hz\]
(D) \[3\times {{10}^{-7}}Hz\]

Answer 1

Hint: Radio waves are a type of electromagnetic radiation best known for communication technologies, such as television, mobile phones and radios. The wavelength of the radio wave has been provided to us and we know that all forms of electromagnetic radiations have the same constant speed. We can use the relation between the wave velocity, wavelength and the wave frequency.

Formula Used:
 \[v=\lambda \times f\]

Complete step by step answer:
We have been given that,
The wavelength of the radio wave \[(\lambda )=10m\]
We know the universal relation between the wave velocity, wavelength and the wave frequency for any wave, which is \[v=\lambda \times f\] where is the velocity of the wave, \[\lambda \] is the wavelength and \[f\] is the wave frequency.
Since radio waves are a form of electromagnetic radiation and all electromagnetic radiations travel with the speed of light, the wave velocity, in this case, will be \[c=3\times {{10}^{8}}m/s\]
The relation between the velocity, wavelength and the frequency now becomes \[c=\lambda \times f\] where the symbols have meanings as discussed above.
Substituting the values, we get
\[\begin{align}
  & 3\times {{10}^{8}}m/s=10m\times f \\
 & \Rightarrow f = 3\times {{10}^{7}}{{s}^{-1}} \\
 & \Rightarrow f = 3\times {{10}^{7}}Hz \\
\end{align}\]
Hence we can say that the frequency of the given radio wave is \[3\times {{10}^{7}}Hz\] and (A) is the correct option.

Additional Information: Radio-wave communication signals travel through the air in a straight line, reflect off of clouds or layers of the ionosphere, or are relayed by satellites in space. They are used in standard broadcast radio and television, navigation and air-traffic control and even remote-controlled toys. Radio waves have the longest wavelength out of all known waves in the electromagnetic spectrum.

Note: In the relation between wave speed, wavelength and frequency, the speed of electromagnetic waves is constant irrespective of any medium, so we can say that frequency and wavelength of electromagnetic waves are inversely proportional to each other. As the wavelength of the wave increases by a factor of ten, the frequency of the wave must decrease by a factor of one-tenth. This is the result we obtained from our calculation. We could also arrive at the same conclusion logically.