Editing Vibrato (section)

=== Leslie speaker ===<!-- TODO: this section needs citations to support its claims - not citations about doppler in general, but about whether it affects the Leslie. See talk page. -->

A [[Leslie speaker]] (best known through its historical and popular association with the [[Hammond organ]]) creates vibrato as a byproduct of tremolo production. As a Leslie speaker is moved by the rotating mechanism on which it is mounted, it moves closer to or farther away from any given object (such as a listener's ears) not also mounted on the mechanism. Because amplitude varies directly with sound pressure (''A = k<sub>1</sub>P'') and sound pressure [[Inverse-square law#Acoustics|varies directly with distance]] (''P = k<sub>2</sub>d''), such that amplitude also varies directly with distance (''[[Elementary algebra#Second method of finding a solution|A = k<sub>1</sub>(k<sub>2</sub>d) = k<sub>1</sub>k<sub>2</sub>d]]''), the amplitude of the sound as perceived by the listener will be greatest when the speaker is at the point in its rotation closest to the listener and least when the speaker is farthest away. Because the speaker is constantly moving either toward or away from the listener, however, the mechanism's rotation is constantly affecting the listener-perceived sound's wavelength by either "stretching" the wave (increasing wavelength) or "squeezing" it (decreasing wavelength) — and because frequency, i.e., pitch, is [[Frequency#Frequency of waves|inversely proportional to wavelength]], such that increasing wavelength decreases frequency and vice versa, any listener for whom the speaker's motion changes the sound's perceived amplitude (''i.e.'', any listener whose distance from the speaker is changing) must also [[Doppler effect|perceive a change in frequency]].