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?

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May 27, 2017

Answer:

#0.0333 "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 = lambdaf#

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

#lambda# (lowercase Greek letter lambda) is the wavelength of the wave, in #"m"#, and

#f# is the frequency of the wave, in #"Hz"# or #"s"^-1#.

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

#lambda = 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.)

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