Audio effects are software (DAW's) or hardware (analog) devices that change the way something sounds.
In physics, an audio effect alters sound waves when applied to an instrument or generally any audio signal sounds. They represent one of the most important studio tools.
One of many obvious examples we could use to illustrate it is how your voice feels in different rooms. If you go into a small room with no windows and start singing, the moment you walk into a spacious hall, your voice has more echoes and generally feels different.
Time-based audio effects: Reverb, Delay, and Echo.
Modulation audio effects: Chorus, Tremolo, Flanger, and Phaser.
Spectral audio effects: Panning and Equalization.
Dynamic audio effects: Compression and distortion.
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