1) wavelength of a 100-MHz sine wave: 3 m
The wavelength of an electromagnetic wave is given by the equation:
[tex]\lambda=\frac{c}{f}[/tex]
where
[tex]c=3\cdot 10^8 m/s[/tex] is the speed of light
f is the frequency of the wave
In this case, the frequency of the wave is:
[tex]f=100 MHz=100 \cdot 10^6 Hz[/tex]
So, the wavelength is
[tex]\lambda=\frac{3\cdot 10^8 m/s}{100\cdot 10^6 Hz}=3 m[/tex]
2) wavelength of a 500-MHz sine wave: 0.6 m
In order to find the wavelength of this wave, we can use the same formula we used previously:
[tex]\lambda=\frac{c}{f}[/tex]
The frequency of the wave in this problem is
[tex]f=500 MHz=500\cdot 10^6 Hz[/tex]
And so, the wavelength is
[tex]\lambda=\frac{3\cdot 10^8 m/s}{500\cdot 10^6 Hz}=0.6 m[/tex]
3) Size of the antenna: 2500 km
First of all, we need to calculate the wavelength of a wave with frequency f=60 Hz:
[tex]\lambda=\frac{c}{f}=\frac{3\cdot 10^8 m/s}{60 Hz}=5\cdot 10^6 m[/tex]
And so, the size of the antenna should be 1/2 of the wavelength, so:
[tex]d=\frac{\lambda}{2}=\frac{5\cdot 10^6 m}{2}=2.5\cdot 10^6 m=2500 km[/tex]
