Question

A certain microwave has a wavelength of 0.032 meters. What is the frequency of the microwave?

Answer 1

`9.4 * 10^8"Hz"`

Explanation:

As you know, wavelength and frequency have an inverse relationship described by the equation

`color(blue)(c = lamda * nu)" "`, where

`lamda` - the wavelength of the wave
`nu` - the frequency of the wave
`c` - the speed of light in a vacuum, approximately equal to `3 * 10^8"m s"^(-1)`

This tells you that short wavelengths are characteristic of high frequency waves, and long wavelengths of low frequency waves.

In your case, the wavelength of the wave is relatively long, so you can expect the frequency to be relatively high. Plug in your values into the above equation and solve for `nu`

`c = lamda * nu implies nu = c/(lamda)`

`nu = (3 * 10^8color(red)(cancel(color(black)("m"))) "s"^(-1))/(0.032color(red)(cancel(color(black)("m")))) = 9.4 * 10^9"s"^(-1) = color(green)(9.4 * 10^9"Hz")`