Question

If you want to tune into a radio station that is carried by a signal with wavelength 3.0 meters, what channel would you choose? Note.. the FM radio dial shows the frequency in Mega-Hertz (MHz).. that is, NPR is 91.7FM operating at 91.7 million cycles per second , 91.7 MHz.

Answer 1

Answer: The radio should be tuned to 100. 0 Mhz.

Step-by-step explanation:

As radio waves are electromagnetic waves, like x-rays, UV rays, and all the wavelengths of visible light, they propagate in the free space at the speed of light: 3. 10⁸ m/s.

At any wave, there is a fixed relationship between the distance travelled by the wave along one cycle (which is called wavelength ) and the speed at which the wave oscillates (which is called the frequency of the wave), with the speed at which the wave propagates, as follows:

λ (wavelength) = v (speed) / f (frequency)

Replacing by the values, and solving for frequency, we have:

f = 3. 10⁸ m/seg / 3 m = 10⁸ 1/sec = 10⁸ Hz = 100. 0 Mhz

This is the radio channel to which must be tuned in order to listen the station with a wavelength of 3 m, in the FM band.