| 11. | This work was taken further by Marin Mersenne who formulated the current law of vibrating strings.
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| 12. | Everything in the universe is made of teeny-tiny vibrating strings each much smaller than an atom.
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| 13. | Machine parts and vibrating strings are common examples.
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| 14. | The two-dimensional analogue of the vibrating string is the vibrating membrane, with the edges clamped to be motionless.
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| 15. | Technically speaking, no amplification occurs, because all of the energy to produce sound comes from the vibrating string.
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| 16. | This measure is the effective length of each of the vibrating strings, not counting compensation for adjusting intonation.
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| 17. | Vincenzo made some substantial discoveries in acoustics, particularly involving the physics of vibrating strings and columns of air.
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| 18. | He and his followers, the Pythagoreans, investigated the harmonics of vibrating strings and laid the foundations of number theory.
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| 19. | The model can be compared to a slowly vibrating string, or a two dimensional surface obeying the wave equation.
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| 20. | Stopping the string closer to the bridge results in higher-pitched sound, because the vibrating string length has been shortened.
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