Question

A communications satellite transmits a radio wave at a frequency of 9.4 x 10^9 Hz. What is the signal’s wavelength? Assume the wave travels in a vacuum. Show your work.

Answer 1

To calculate this we will use the light equation:
$c=$λ$*f$

We have Frequency $f=9.4* 10^{9}Hz$.
We know that speed of light in vacuum is $c =3.8* 10^{8} m/s$.
Since a unit of speed of light is m/s, we can change the unit of frequency Hz to 1/s, since Hz means cycles per second (f=1/T).

So:
$f=9.4* 10^{9}1/s$
$c =3.8* 10^{8} m/s$

$c=$λ$*f$
⇒ λ$= \frac{c}{f}$
⇒ λ$= \frac{3.8* 10^{8}}{9.4* 10^{9}}$
⇒ λ$=0.04 m$