Compute the wavelength of the radio waves from the following stations. (a) an AM station operating at a frequency of 800 kHz m

Question

(b) an FM station with a frequency of 98.9 MHz

m

Answer 1

To answer this question, you need to know the constant for the speed of light and the frequency vs. wavelength equation:

c (speed of light) = 3 x 10⁸ meters/second

Equation:

wavelength (nm) = speed of light / frequency (Hz)

The trick to this problem (as with most in physical science and physics) is to watch the units: they have to match exactly or this does not work. Your word problem gives units of kHz, which do not match those for this equation. (Also, not sure why there is an "m" after the Hz unit in your word problem, as meters are not allowed as units of frequency. Perhaps the problem is requesting you to convert your wavelength answers to meters?)

A) Convert kHz to Hz by multiplying by 1000 --> 800 kHz = 800,000 Hz

wavelength (nm) = 3 x 10⁸ m/s / 800,000 Hz

wavelength = 1000 nm

(In case the problem does want wavelength in meters, we can do that conversion as well)

1000 nm / 1,000,000,000 = 0.000001 meters or 1 x 10^-6 m (final answer in meters)

B) Conver 98.9 MHz to Hz --> 98.9 MHz x 1,000,000 = 98,900,000 Hz

wavelength (nm) = 3 x 10⁸ m/s / 98,900,000 Hz

wavelength = 3 nm

Convert to meters (if needed)

3 nm / 1,000,000,000 = 3 x 10^-9 m