Question

AIR service on Vividh Bharati is transmitted on 219m band. What is its transmission frequency in Hertz?

Answer 1

Hint:Recall the relation between wavelength, frequency and velocity of the electromagnetic wave. The frequency of the electromagnetic wave is inversely proportional to the wavelength. For the transmission of information by Vividh Bharati, radio waves are used.

Complete answer:
We have given the wavelength of the signal being transmitted and it is \[\lambda = 219\,{\text{m}}\].We have the relation between wavelength, frequency and velocity of the electromagnetic wave,
\[c = f\lambda \]
Here, c is the speed of the electromagnetic wave, f is the frequency and \[\lambda \] is the wavelength of the wave.
Rearranging the above equation for frequency f, we get,
\[f = \dfrac{c}{\lambda }\]
Substituting \[c = 3 \times {10^8}\,{\text{m/s}}\] and \[\lambda = 219\,{\text{m}}\] in the above equation, we get,
\[f = \dfrac{{3 \times {{10}^8}}}{{219}}\]
\[ \therefore f = 1.37 \times {10^6}\,{\text{Hz}}\]

Thus, the frequency of the radio wave that is being transmitted is \[1.37 \times {10^6}\] Hertz.

Additional information:
For the transmission of information, radio waves are used. Transmitting information over two devices using radio waves requires a transmitter and a receiver. The function of the transmitter is to encode the signal like audio or video signal into a sine function and transmit it into the air as radio waves. The receiver on other base stations receives this signal and decodes it again into audio or video format. The radio wave is one type of electromagnetic wave and it travels with the speed of light. Thus, the speed of light and speed of radio waves is the same.

Note:The speed of a radio wave is the same as speed of light. The speed of light depends upon the refractive index of the medium. Therefore, if the radio wave travels through a medium other than air, its speed decreases and so the wavelength.