AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of $3.0 \times 10^8 \textrm{ m/s}$. What are the wavelengths of these signals? On FM the frequencies range from 88 MHz to 108 MHz (megahertz) and travel at the same speed. What are their wavelengths?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The speed of a wave is its frequency times its wavelength and we can divide this formula by f on both sides. And we get wavelength is the wave speed divided by its frequency. So, for AM signals, the minimum wavelength is going to be 3 times 10 to the 8 meters per second speed divided by its maximum frequency of 1600 times 10 to the 3 hertz. We have to convert the kilohertz into hertz and that is 190 meters for the minimum wavelength. And then for the maximum wavelength we get the same speed divided by 550 kilohertz or 550 times 10 to the 3 hertz which gives 550 meters. For FM signals we have that the maximum wavelength is going to be 3 times 10 to the 8 divided by 88 times 10 to the 6 hertz, it's megahertz, so that means times 10 to the 6. That gives 3.4 meters. And then divide that speed by 108 times 10 to the 6 to get to 0.8 as the minimum wavelength for FM signals.