How deeply does Learn Haskell by Example cover sinusoidal function?

Defines the waveform, explains period scanning and frequency, and implements tone generation without developing further mathematics.

Sinusoidal function

As explained in Learn Haskell by Example

A sine wave is a periodic waveform whose value follows the mathematical sine function.

A sinusoidal function generates a repeating sine-wave sample from a position within one period. In Haskell, model a waveform as `Double -> Sample`; `sin t = Prelude.sin (2 * pi * t)` maps an input between 0 and 1 to the wave's sample value, typically between -1 and 1. section 10.1.2

Use the function as part of a digital signal:

Scan through positions from 0 to 1 to trace one period of the waveform. section 10.1.2

Generate a tone

A five-second 220 Hz tone can be created with `tone sin 220 5`. Combining it with other waveforms and passing the result to `writeWav` produces an audible WAV file.

How Learn Haskell by Example covers it

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Also explained in

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Building Quantum Software with PythonA sinusoid is a waveform described by a sine or cosine function and characterized by a frequency and phase.

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Related concepts

math.sinproduced by · Math.sin is a JavaScript Math method that returns the sine of an angle expressed in radians.
positional embeddinguses · A positional embedding is a learned or fixed representation that encodes an element’s position or order in a sequence and is incorporated into its content representation.
amplitudeconfigured by · Amplitude is the maximum magnitude of an oscillating quantity's displacement from its equilibrium or reference value.
frequencyconfigured by · Frequency is the count or rate at which an item, event, outcome, or periodic cycle occurs within a specified collection or interval.
sound wavekind of · A sound wave is a mechanical disturbance that propagates through a medium and can be perceived as sound.
Fourier transformproduced by · The Fourier transform is a mathematical transformation that represents a function or signal as constituent sinusoidal components organized by frequency.

This explainer was generated by Manning's knowledge graph from the text of Learn Haskell by Example. The section links point to the parts of the book it draws on.