# Microwaves travel at the speed of light, 3.00 times 10^8 m/s. When the frequency of microwaves is 9.00 times 10^9 Hz, what is their wavelength?

May 27, 2017

$0.0333 \text{m}$

#### Explanation:

We're given a wave's speed and its frequency, and we're asked to calculate its wavelength.

The wavelength-frequency relationship of a periodic wave is represented by the equation

$c = \lambda f$

where
$c$ is the speed of light in vacuum, equal to $299 , 792 , 458 \text{m"/"s}$ (given to us with $3$ significant figures),

$\lambda$ (lowercase Greek letter lambda) is the wavelength of the wave, in $\text{m}$, and

$f$ is the frequency of the wave, in $\text{Hz}$ or ${\text{s}}^{-} 1$.

Since we're trying to find the wavelength, let's rearrange this equation to solve for wavelength, $\lambda$:

$\lambda = \frac{c}{f}$

Plugging in our known variables, we have

lambda = (299,792,458 "m"/cancel("s"))/(9.00 xx 10^9 cancel("s")^-1) = color(red)(0.0333 "m"

(You don't need to use the exact value for $c$, but it could give a more exact answer. It regardless gives you the same wavelength.)