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.

Respuesta :

To calculate this we will use the light equation:
[tex]c=[/tex]λ[tex]*f[/tex]

We have Frequency [tex]f=9.4* 10^{9}Hz [/tex].
We know that speed of light in vacuum is [tex]c =3.8* 10^{8} m/s [/tex].
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:
[tex]f=9.4* 10^{9}1/s [/tex]
[tex]c =3.8* 10^{8} m/s [/tex]

[tex]c=[/tex]λ[tex]*f[/tex]
⇒ λ[tex]= \frac{c}{f} [/tex]
⇒ λ[tex]= \frac{3.8* 10^{8}}{9.4* 10^{9}} [/tex]
⇒ λ[tex]=0.04 m[/tex]

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