Our local public radio station (KJZZ) broadcasts at a frequency of 91.5 MHz.

(a) What is the wavelength of the radio waves emitted by the KJZZ broadcast antenna? Give your answer in meters.

m

(b) What is the wavelength of the radio waves emitted by the antenna of an AM station broadcasting at a frequency of 1060 kHz?

Answer: (a) The wavelength for KJZZ is 3.2787 * 10^-3m

(b) The wavelength emitted by the antenna of an AM station is 283.02m

Explanation:To calculate wavelength, the formula is given as;

Wavelength = speed of wave (v) / frequency (f)

Note: Speed of wave = 3*10^8

(a) Using the formula given above,

Wavelength = Speed of wave (v) / frequency (f)

Where speed of wave=3*10^8

Frequency = 91.5MHz (whi

a) 3.3 m b) 283 m

Explanation:

a) As radio waves are just another representation of electromagnetic waves, at some distance of the antenna, they behave like plane waves, and keep constant the following relationship between frequency, wavelength and wave speed:

λ*f = v

For an electromagnetic wave, v is just the light speed in the medium where the wave is propagating, which for clear air can be approximated by the value of the speed of light in vacuum, c, as follows:

c = 3*10⁸ m/s

⇒ λ = c/f = 3*10⁸ m/s / 91.5*10⁶ Hz = 3.3 m

b) As radio waves in the AM range behave exactly like ones in the FM range (at a distance from antenna larger than a few wavelengths), same considerations apply, so we can find the wavelength λ using the same equation as above, for the 1060 Khz frequency:

⇒ λ = c/f = 3*10⁸ m/s / 1060*10³ Hz = 283 m.