Finding frequency of microwaves

[songoku]

Homework Statement

A strip of wet cardboard is fixed on the bottom of a microwave oven. The microwave oven is turned on for a short time. When the card is removed a pattern of dry spots is observed on the cardboard. This is because a standing wave is set up inside the oven. The dry spots are measured and found to occur at 14 mm, 86 mm, 156 mm, 225 mm and 293 mm from the end of the strip.
What is the frequency of the microwaves?

Relevant Equations

d sin θ = n.λ

fringe separation = λ L / d

I thought 14 mm, 86 mm, 156 mm, 225 mm and 293 mm are the position where constructive interference happens 14 mm is the position of 1st maxima, 86 mm is the position of 2nd maxima and etc (measured from a certain position of center maxima)

But when I used that numbers to calculate the fringe separation, I got different results:
86 -14 = 72 mm
156 - 86 = 70 mm
225 - 156 = 69 mm
293 - 225 = 68 mm

So I think I am wrong, those numbers are not the position of constructive interference.

How to approach this question? Thanks

 

[BvU]

Hi,

You mention fringes, but I suspect (well, the problem statement explicitly says it) the pattern is a consequence of standing waves: different relevant equation.

I don't understand your "I got different results" when the variance is so small: the dry spots are at very regular intervals indeed !

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[songoku]

Hi,

You mention fringes, but I suspect (well, the problem statement explicitly says it) the pattern is a consequence of standing waves: different relevant equation.

I don't understand your "I got different results" when the variance is so small: the dry spots are at very regular intervals indeed !

View attachment 285882

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Is it correct to think the dry spot as the antinode of a standing wave? Maybe because at antinode the displacement will be maximum so water molecule will be moved away from that spot, leaving dry spot.

Thanks

 

[BvU]

Any reason for this apparent doubt ?

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[haruspex]

so water molecule will be moved away from that spot

Yes, into the air!

 

[Delta2]

Is it correct to think the dry spot as the antinode of a standing wave? Maybe because at antinode the displacement will be maximum so water molecule will be moved away from that spot, leaving dry spot.

Thanks

It is a standing electromagnetic (micro) wave that meets water molecules. The way water molecules interact with electromagnetic waves in the microwave frequency is that they absorb energy from the wave which is converted to heat, the water is heated and it might evaporate if the heat is too strong at that point. The dry spots are because the water has been evaporated by the electromagnetic standing wave and this happens at the points where the standing wave is the strongest, that is at antinodes.

 

[songoku]

Any reason for this apparent doubt ?

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That is because I am not sure how to visualize the question. After you said I should use different relevant equation, I thought about using path difference = n.λ for constructive interference but since I do not know how to visualize the question, I do not know the location of the source of the stationary wave to determine the path difference. Basically my doubt arises because my basic is not strong. I am even surprised the antinode thing crossed my mind.

Thank you very much for the help and explanation BvU, haruspex and Delta2

 

[Delta2]

If I tell you that you had a standing wave in a rope and the antinodes are approximately every 70mm how would you find the frequency of the standing wave

 

[BvU]

If I tell you that you had a standing wave in a rope and the antinodes are approximately every 70mm how would you find the frequency of the standing wave

With difficulty. But the wavelength is easy !



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[Delta2]

With difficulty.

Even if I tell you the speed of the waves in the rope?

 

[songoku]

If I tell you that you had a standing wave in a rope and the antinodes are approximately every 70mm how would you find the frequency of the standing wave

I know how to solve the question now. Find the wavelength based on the distance between two adjacent antinodes then find the frequency using the speed of microwaves

 

[berkeman]

Find the wavelength based on the distance between two adjacent antinodes

Just to check, how many wavelengths apart are two adjacent antinodes in a standing wave?

 

[songoku]

Just to check, how many wavelengths apart are two adjacent antinodes in a standing wave?

half wavelength

 

[songoku]

Thank you very much BvU, haruspex, Delta2 and berkeman

 

[rsk]

We do this experiment every year in class, except with a bar of chocolate instead of the damp card, and we bill it as measuring the speed of light. The chocolate melts at the position of the antinodes and we measure the gaps between these.

As above, the difference in the gaps is too small to be significant. Between 14mm and 293mm there are 5 antinodes or 4 antinode-antinode gaps. So you can find what this gap is on average, then calculate the wavelength of the microwaves from that. We use that with the frequency on the plate on the back of the microwave to find the speed of the waves.