Generative art as a physics lesson - oscillation

11 Jul 20241 EDITIONS

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For start

I want to start with the fact that the entire text is written by the same person who created oscillation | 1. It carries an interesting and entertaining function by describing the nature of the waves that are in the artwork.

Not the same, but natural. We are talking about physics, not algebra.

We are talking about waveforms. This is mostly a popular topic for electricians, because different devices require different types of electrical current.

Sine wave

Sine wave using p5.js lib. Shown in P5.js web editor.

Math (amplitude formula):

x(t)=A\sin(\omega t+\varphi _{0}),

Form:

A sine wave has a smooth, periodic shape that resembles a smooth rise and fall. It increases to a maximum amplitude, then returns to zero, decreases to a minimum amplitude, and returns to zero again, repeating this cycle.

Examples of use:

Alternating Current (AC) Electrical Signals: Most electrical networks use a sinusoidal form of current because it provides an even distribution of energy.

Sound waves: Musical notes and other pure sounds have a sinusoidal shape, which gives them a timbre that is pleasing to the ear.

Vibrations: In many mechanical systems, vibrations can have a sinusoidal shape, which ensures the smoothness of their operation.

Features:

Signal purity: A sine wave contains only one fundamental frequency with no additional harmonics, making it very clean.

Spectrum: There is only one frequency in the spectrum of a sine wave, which makes it easy to filter and process such signals.

Rectangular wave

Rectangular wave using p5.js lib. Shown in P5.js web editor.

Maths (heaviside function):

x(t)=2\ A\sum _{n=-\infty }^{\infty }\left[h\left({\frac {t}{T}}-n\right)-h\left({\frac {t}{T}}-n-{\frac {1}{S}}\right)\right]-1,

Form:

A rectangular wave consists of alternating high and low levels that change instantly. Imagine that you are constantly turning the light on and off: the light is either on or off, and the changes happen instantly.

Examples of use:

Digital technology: All digital devices use square waves to transmit data in the form of binary codes (0 and 1).

Synthesizers: In music, square waves are used in electronic instruments to create a specific, richer and sharper sound.

Pulse signals: In many control systems, rectangular pulses are used for a clear signal about a change in the state of the system.

Features:

Multifrequency: A square wave contains not only the fundamental frequency, but also a large number of harmonics, which gives it a richer and sharper character.

Spectrum: The spectrum of a square wave consists of the fundamental frequency and odd harmonics, which makes it rich in frequency components.

About both

Similarities:

Both waves are periodic, that is, they repeat at a certain interval.

They can transmit information and be used for various purposes, both in technology and in nature.

Differences:

Shape: A sine wave is smooth and smooth, while a square wave has sharp transitions between highs and lows.

Signal purity: A sine wave is pure and contains only one frequency, while a square wave has many additional frequencies (harmonics), making it more complex.

Applications: A sine wave is suitable for transmitting pure signals such as sound or alternating current, while a square wave is better suited for digital signals and control systems.

Why talking about it?

I believe that art (anything) can have not only an aesthetic but also an entertaining and cognitive function. I hope that at least the presence of this text entertained you, and maybe interested you in reading it.

Credits:

- Pavlosky J. (Twt - @pavl_bpr)

- UzhN University

- Pysics for students Bushok G.F., Wenger E.F.

Artwork: