earth’s normal modes. fundamentals and harmonics remember, a guitar string can have a fundamental...
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![Page 1: Earth’s Normal Modes. Fundamentals and Harmonics Remember, a guitar string can have a fundamental (lowest tone) and many harmonics (integer level multiples)](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d8b5503460f94a72f38/html5/thumbnails/1.jpg)
Earth’s Normal Modes
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Fundamentals and Harmonics
Remember, a guitar string can have a fundamental (lowest tone) and many harmonics (integer level multiples). They combine constructively and destructively to give the guitar its sound.
![Page 3: Earth’s Normal Modes. Fundamentals and Harmonics Remember, a guitar string can have a fundamental (lowest tone) and many harmonics (integer level multiples)](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d8b5503460f94a72f38/html5/thumbnails/3.jpg)
Fourier Analysis
When a guitar string is plucked, we can see its fundamental and harmonics using a Fourier Analysis shown here.
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Normal Modes
Just like a guitar string, a strong earthquake can make Earth with a fundamental frequency with overtones.
Spheroidal (radial motion)
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Normal Modes
Normal modes can also occur in toroidal motion
![Page 6: Earth’s Normal Modes. Fundamentals and Harmonics Remember, a guitar string can have a fundamental (lowest tone) and many harmonics (integer level multiples)](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d8b5503460f94a72f38/html5/thumbnails/6.jpg)
Toroidal Normal Modes
Shearer Ch.8.6Lay and Wallace, Ch. 4.6
Indexes describe spherical harmonics
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Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html
Free Oscillations l=1 m=1
![Page 8: Earth’s Normal Modes. Fundamentals and Harmonics Remember, a guitar string can have a fundamental (lowest tone) and many harmonics (integer level multiples)](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d8b5503460f94a72f38/html5/thumbnails/8.jpg)
Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html
Free Oscillations l=1 m=2
![Page 9: Earth’s Normal Modes. Fundamentals and Harmonics Remember, a guitar string can have a fundamental (lowest tone) and many harmonics (integer level multiples)](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d8b5503460f94a72f38/html5/thumbnails/9.jpg)
Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html
Free Oscillations l=1 m=3
![Page 10: Earth’s Normal Modes. Fundamentals and Harmonics Remember, a guitar string can have a fundamental (lowest tone) and many harmonics (integer level multiples)](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d8b5503460f94a72f38/html5/thumbnails/10.jpg)
Earth’s Normal NodesDid you notice in the previous animations how some parts of the Earth moved more than other? Why is this?
Reflected waves create Constructive and Destructive Interference
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Fundamentals and HarmonicsThe periods of oscillation are all greater than 10 minutes and deflect Earth’s surface only the distance of the width of a human hair
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Why study normal modes???Seismologists all around the world study Earth’s normal modes to determine the internal structure of Earth and help determine how the Earth was formed!