Question

You have a microwave generator that can produce microwaves at any frequency between $1GHz$ and $10GHz$. The microwave radiation enters a $10cm$ long cylinder with reflective end caps, as shown in the figure. What frequency of the microwave generator (in $GHz$) will produce the lowest-order standing wave with an antinode (maximum) in the center of the cavity? Note that with reflectors at both ends, the electromagnetic standing wave acts just like the standing wave on a string that is tied at both ends. Take velocity of waves as $3\times {10}^{8}m/s$.

Answer 1

Given, velocity of the wave,
$v=3\times {10}^{8}m/s$
Length of the cylinder, $L=10cm$

For the overtone at the center of cavity,
$\lambda =2L=0.2m$

So, the frequency produced by the generator,
$f=\frac{v}{\lambda }$
$f=\frac{3\times {10}^8}{0.2}$
$=1.5\times {10}^{9}Hz$
$=1.5GHz$

Final answer: (1.50)