*
A microwave generator can producemicrowaves at any kind of frequency between 10.0 GHz and also 20.0 GHz . As thefigure shows, the microwaves are aimed, through a small hole, intoa "microwave cavity" that consists of a 10.0 cm-long cylinder withreflective ends.

You are watching: Microwaves pass through a small hole into the “microwave cavity” of the figure.

Part AWhich frequencies in between 10 GHz and 20 GHz will develop standingwaves in the microwave cavity?Enter her answers numerically in raising order separated bycommas.f = _________________________GHzPart BFor i m sorry of these frequencies is the cavity midpoint anantinode?Enter your answers numerically in raising order separated bycommas.fa = ___________________________GHz


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Homework Answers
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prize #1
Concepts and reason

The principle used to settle this difficulty is standing waves on a string and also microwaves.

Use the size of the cavity to discover the expression for the wavelength that develops standing waves.

Use the relation between the size of the cavity and also the speed of the wave to find the relation between the frequencies of the matching waves.


Fundamentals

Assume the the microwave cavity together a close up door pipe, because the 2 ends are reflective.

Expression because that the wavelength that forms standing waves is together follows:

*

Here,

*
is the wavelength that develops standing waves, l is the size of the cavity, and also n is the order.

Expression because that the frequency the the tide is together follows:

*

Here, f is the frequency that the microwave and also c is the speed of the light.


(A)

Expression for the frequency of the wave is together follows:

*
…… (1)

Expression because that the wavelength that creates standing tide is as follows:

*

Replace

*
for
*
in Equation (1) to solve for
*
.

*

Case 1:

The frequency for the matching wave of stimulate

*
is together follows:

*

Here,

*
is the frequency because that the corresponding wave of bespeak
*

Substitute

*
because that c,
*
for n, and
*
because that L.

*

Case 2:

The frequency for the equivalent wave of order

*
is together follows:

*

Here,

*
is the frequency because that the equivalent wave of bespeak
*
.

Substitute

*
because that c,
*
because that n, and also
*
for L.

*

Case 3:

The frequency for the corresponding wave of stimulate

*
is together follows:

*

Here,

*
is the frequency for the corresponding wave of stimulate
*
.

Substitute

*
because that c,
*
for n, and also
*
for L.

*

Case 4:

The frequency because that the equivalent wave of bespeak

*
is as follows:

*

Here,

*
is the frequency for the equivalent wave of bespeak
*
.

Substitute

*
because that c,
*
because that n, and
*
for L.

Case 5:

The frequency for the corresponding wave of stimulate

*
is as follows:

*

Here,

*
is the frequency because that the equivalent wave of stimulate
*
.

Substitute

*
for c,
*
for n, and
*
for L.

*

Case 6:

The frequency for the corresponding wave of order

*
is as follows:

*

Here,

*
is the frequency because that the corresponding wave of stimulate
*
.

Substitute

*
because that c,
*
for n, and also
*
because that L.

*

Case 7:

The frequency because that the equivalent wave of order

*
is as follows:

*

Here,

*
is the frequency for the matching wave of bespeak
*
.

Substitute

*
for c,
*
for n, and also
*
because that L.

*

Therefore, the frequencies are ranked ~ above the basis of raising order together follows:

*
.

(B)

Here, there space seven various frequencies of was standing waves.

The even variety of n create a node point, if odd number of n create antinodes.

The frequencies that have actually the midpoint called as antinodes that room as follows:

*
,
*

*
,
*

,

*

*
,
*

Ans: part A

The increasing order that the frequencies in between

*
and also
*
in the microwave cavity that creates standing waves space
*
,
*
,
*
,
*
,
*
,
*
,
*
.

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Part B

The raising order the the frequencies between

*
and
*
is the microwave cavity midpoint an antinodes room
*
,
*
,
*
,
*
.