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6

Let's look at frequency instead of notes. Let's say the string has a natural frequency of $100 Hz$ and that harmonics are present when you pluck it. Then, the frequency content of the sound will be of the form: $a_1 \cdot 100 Hz + a_2 \cdot 200 Hz + a_3 \cdot 300 Hz + ...$ Now, let's say you fret this string halfway such that the natural frequency ...

6

A guitar string produces harmonics because it vibrates in a non-linear fashion. An electronic oscillator can be made to generate a much purer form of vibration (near sinusoidal) than a mechanical device such as the guitar string. Hence its harmonic level, while not zero, is much lower. For example, the harmonic distortion of a guitar string is probably on ...

4

Frequency is just a way of analyzing a time dependent motion. Consider plucking a string by first pulling one point on the string away from its equilibrium. The string shape will be like a triangle, two straight bits of string coming away from where your finger is holding the string, but meeting at a slight angle where your finger holds the string. That ...

2

Hopefully David Bar Moshe can give a more rigorous explanation in terms of cohomology, but I have the following intuitive understanding of the difference between the two situations. In the Aharonov-Bohm effect, the particle is constrained to move around an (effectively) infinite solenoid. It then suffices to consider a problem on a plane, but with a hole in ...

1

I'm not qualified to answer this question in detail...but I'd like to point out some things I've learned lately that may be helpful. Hilbert space is useful when you need an infinite dimensional space to characterize what you are studying and where each mode is orthogonal to the others. Great for Quantum Mechanics... Where I work, images, that is 2D ...

1

You can send sound waves of any wavelength into your instrument, but the trouble is that only specific wavelengths correspond to standing waves. The other waves will just die out because of destructive interference. When your sound wave collides with the closed end of a pipe for instance, it gets reflected back. If the wavelength is not right, the ...

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