Chapter 17: Q. 13 (page 483)

Microwaves pass through a small hole into the “microwave cavity” of FIGURE EX17.13. What frequencies between 10 GHz and 20 GHz will create standing waves in the cavity?

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Step by step solution

The length of the microwave cavity is $L = 10 c m = 0.10 m$

There are reflectors at both ends, so the electromagnetic standing wave acts like the standing wave on a string that is tied at both ends.

The electromagnetic waves of all frequencies travel at the speed of light c.

The frequencies of the standing waves are given by

$f_{m} = m \frac{v_{l i g h t}}{2 L} = m \frac{c}{2 L}$

Substitute the given values

$f_{m} = m (\frac{3 \times 10^{8}}{2 \times 0.10}) = m (1.5 \times 10^{9}) = 1.5 m G H z$

The generator can produce standing waves at any frequency between $10 G H z$ and $20 G H z$ .

The table below shows the frequencies produce by the generator between $10 G H z$ and $20 G H z$ .

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