(a) 0.0026 Hz
The relationship between frequency and wavelength for an electromagnetic wave is
[tex]f=\frac{c}{\lambda}[/tex] (1)
where
[tex]c=3.0\cdot 10^8 m/s[/tex] is the speed of light
f is the frequency
[tex]\lambda[/tex] is the wavelength
For the wave in the problem, the wavelength is [tex]1.8\cdot 10^4[/tex] Earth radii. The Earth radius is
[tex]R=6370 km = 6.37\cdot 10^6 m[/tex]
so the wavelength would be
[tex]\lambda = (1.8\cdot 10^4 )(6.37\cdot 10^6 m)=1.14\cdot 10^{11}m[/tex]
So by using eq.(1) we find the frequency:
[tex]f=\frac{3\cdot 10^8 m/s}{1.14\cdot 10^{11}m}=0.0026 Hz[/tex]
(b) 384.6 s
The period of a wave is given by:
[tex]T=\frac{1}{f}[/tex]
where
T is the period
f is the frequency
For the wave in the problem,
f = 0.0026 Hz
so the period is
[tex]T=\frac{1}{0.0026 Hz}=384.6 s[/tex]
