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2

There is an equation that translate properly the situation of a string under a pulse of frequency $\omega$ at the point $x_0$ of the string. $$ \rho\frac{d^2y}{dt^2}=T\frac{d^2y}{dx^2}+\kappa \delta(x-x_0)\sin(\omega t) $$ this equation is nothing more than an application of the Newton's second law. The first term is the $ma$ part of the $f=ma$. Here ...


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I would say it has to do with energy/information conservation laws. You can imagine a wave (be it electromagnetic or vibrations on a string) is propagating through a medium. The energy of such a wave is given by: Classical harmonic oscillator (pendulum or vibrating string) $$ U = \frac{1}{2}kx^2 $$ where $x$ is displacement from the steady-state rest ...


1

All materials have a resonant frequency Well, sort of. In general, complicated structures will have many resonant frequencies where the amplitudes of any oscillations will have local maxima. However, one of the jobs of structural engineers, and I would assume this would apply to aeroplanes too, is to find these frequencies and make sure that either (a) ...


1

You say: All materials have a resonant frequency but this is at best an oversimplification. Any system has a set of normal modes and if you apply driving force at a frequency that matches a normal mode then you will get a resonance. However for any system significantly more complicated than a tuning fork there are many normal modes and non-linearities ...


3

A few observations. First - if you record sound for a short time, the bandwidth of the sample will result in a smearing of the peaks. This only really matters if the sample is very short - with a 1 second sample you would have 1 Hz resolution, but if you sample for 0.01 second, the bandwidth is 100 Hz. Second, you are using a scale that is quite compressed ...


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Obviously it would require more effort to build a cyclotron that has to change the frequency of the alternating current while the particle accelerates. That the frequency doesn't depend on the particle's energy (in the non-relativistic regime) means you don't need to change it during operation.


13

i've programmed some shepard tones and even a voice generator. The human voice can't make that sound for the same reason that a single or even 3 trumbones couldn't make it. if you had 12 trumbones you could conceivably put them on a wheel system so that the pitch of each is increased and when the top one reaches to top is muted and send down to the lowest ...


19

The human voice box produces a fundamental frequency and its harmonics because the mechanism is like that of a relaxation oscillator. However, we have limited control over the relative amplitude of the harmonics (we do have some - that is how we change the "color" of a tone we sing, and the sound of vowels). In order to produce the Shepard scale, you need ...


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I'll start with the second part of your question: If the frequency of the force, $\omega$, goes to zero then it is just a constant force - there won't be any oscillation! Since there is no oscillation the force and the motion will be in phase (by default). To answer why the force and motion can HAVE separate phases in the first place we look at the ...



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