Tell me something cool about sinusoids
>>16811781The sum of every value from tan(0) to tan(π) is infinity
>>16811781When you plot a sinusoid in polar coordinants, you get a trigonometric rose.Pic related is variations dependent on the angular frequency of the sinusoid.
>>16811782This is not true. For any value y=tan(x) 0<x<π there will be tan(x')=-y in this interval, thus the sum is zero
Mine are clogged.
>>16811781If you reflect the sine function about the x-axis,then about the y-axis, you get the same function back[math] -\sin(x)=\sin(-x) [/math]
>>16811781Simple Harmonic Motion(SHM), as described most often by a sin wave, can be found throughout virtually the entire natural world and form of manmade machines, light, sound, water, etc.... Anything that goes up/down, in/out, +/-, at a regular rate is a sin wave, and it's these waves, the disturb "fields" that make "particles" with forms like waves that form atoms that form "stuff n' sheeeit". Every "thing" really do just be vibing at the frequency of different sin waves.
>>16811781Springs/spirals are just 3-D sin waves and do a great job of replicating them in a lab. If let a spring bob up and down with a pen attached to the end an drag paper under it to show the passage of time, you'll get the pic from OP. Up, down, up, down, boing, boing, boing. The faster it goes the "higher in pitch" it would sound, and the slower the "lower in pitch" it would sound. Same with the energy of the "particle"/light it represents. High freq = high energy. All just different ways of describing and conceptualizing the shape of the sin waves IRL.
>>16811786If you do this to sum of sinusoids, on every frequency used in sum it'll do this "pointing to the right" effect you can see on main diagonal. That's basically how Fourier transform works.
>>16811781this with a frequency decay and a peak height decay is a drop of water's pattern when it hits waterwhich is also the pattern that schizophrenia follows when you quit your medication, maximums (minimums somehow don't count) being a psychotic episode
Painfully close.The roses shown are represented in polar form with the equation [math]r=cos(\frac{a}{b}Θ)[/math].In the complex plane, the same could equivalently be written as[eqn]z=cos(\frac{a}{b}t)e^{(ift)}[/eqn]where f is your wrapping frequency and you set it to 1. In other words: polar coordinates are equivalent to the complex domain of the fourier transform only when the wrapping frequency is equal to 1. However, we, at least visually, can also get the same output from setting the wrapping frequency to the reciprocal of a/b and the frequency of the sinusoid equal to 1 as shown in pic related.This reciprocal behavior is why we end up with the "rightward pointing" effect when the wrapping frequency and sinusoidal angular frequency match.(note, I'm only displaying half of the rose in the complex domain to emphasize the overlap).
>>16811781Polarimetry (measuring an enantiomeric excess of a chiral compound in solution by detecting the degree of rotation of a linearly polarized beam of light) works because a 2D sine wave can be represented as a linear combination of a left-handed and right-handed 3D helix, or two complex sine waves with opposite complex magnitudes.A phase shift between these two basis helices results in a rotation about the axis of propagation.Chiral compounds have no rotational or reflective symmetry, hence the electron density around the chiral center has a helical structure, and R/S chiral compounds will have different absorption coefficients for left-handed and right-handed circularly polarized light. This means that the speed of light for left-handed and right-handed circularly polarized photon will be different through a solution with an enantiomeric excess.Because a linearly polarized photon is in a state of superposition composed of both a left-handed and right-handed circularly polarized state, the difference between the speeds of light of the basis states through a chiral medium result in a rotation of the plane of polarization of the photon due to a phase shifting of the basis states.
>>16814188[eqn] z=cos(\frac{a}{b}t)e^{(ift)} [/eqn]
>>16811782>tell me about the sin function>he tells you about the tan functionWTF?
>>16811781I was gonna poast about Legendre polynomials but this thread makes me realize you guys are all larping high schoolers
>>16818390Welcome to /sci/
>>16818390I am masters student, but I stopped understanding in highschool, so I don't understand basic undergrad stuff like divergence and curl
>>16814245>literally thought this was a useless obscure fact you only learn in grad level QM>A popsci video about it pops up on my YouTube recommendations a few days after posting thiswtf
>>16818800>he thinks Fourier transforms are grad level QMngmi bro
>>16818803>He thinks Fourier is trivial
>>16811781The product of two sine/cosine waves of different frequencies is equal to a linear combination of sine/cosine waves of other frequencies. Two neat things about this>The set of linear combinations of sines and cosines is a subring of the ring of functions>You can hear this with your ears: if you modulate the volume of a sine wave by another sine wave you percieve it as two different tones
>>16818969oh my fucking godddddd
>>16811781They're all u need man
>>16811781\[\int_0^{\pi} \sin(mx)\, \sin(nx)\, dx =\begin{cases}0, & \text{if } m \ne n \\\dfrac{\pi}{2}, & \text{if } m = n\end{cases}\]
>>16813643That's odd
>>16811781If you play a sinewave on your phone, and put it in the other room or in the fridge, the sound won't get muffled, it will just get quieter
>>16811781you can represent them as a rotating line intersecting a cylinder and totally confuse yourself with imaginary numbers so that's nice
>>16814245electrons themselves can become twisted by helical lighthttps://www.science.org/doi/10.1126/science.adp9143
euler's indetity
>>16811781they perfectly cover the energy space.
>>16822568yeah maybe if reverberations didn't exist, and its not like most speakers can actually output a single frequency without introducing harmonicsbut sure you theoretically cant filter a single sine way down any further since its ideally a single frequency with no harmonics. muffling isn't just the concept of filtering though unless you live in an an-echoic chamber
>>16814188nice
>>16811781If you plotted the rhythm with which I bang OP's mother over time, it would create a sin wave.
