Answer:
0.53 m
[tex]2.8301886792\times 10^{13}\ Hz[/tex]
283286118.98
Explanation:
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
m = Mode = 100000
[tex]\lambda[/tex] = Wavelength = [tex]10.6\ \mu m[/tex]
Length of a tube is given by
[tex]L=m\dfrac{\lambda}{2}\\\Rightarrow L=100000\dfrac{10.6\times 10^{-6}}{2}\\\Rightarrow L=0.53\ m[/tex]
The length of the tube is 0.53 m
Frequency is given by
[tex]f=\dfrac{c}{\lambda}\\\Rightarrow f=\dfrac{3\times 10^8}{10.6\times 10^{-6}}\\\Rightarrow f=2.8301886792\times 10^{13}\ Hz[/tex]
The frequency is [tex]2.8301886792\times 10^{13}\ Hz[/tex]
Time taken to bounce back and forth
[tex]t=\dfrac{2L}{c}\\\Rightarrow t=\dfrac{2\times 0.53}{3\times 10^8}\\\Rightarrow t=3.53\times 10^{-9}\ s[/tex]
Round trips in one second
[tex]n=\dfrac{1}{3.53\times 10^{-9}}\\\Rightarrow n=283286118.98[/tex]
The number of round trips is 283286118.98
