A common example is the phase difference between the input signal and output signal after it passes through a circuit, cable, or PC board trace. Retrieved More examples are given below. Now, at the same time as moving it side-to-side, if you moved the pencil up-and-down with a different sinusoidal motion, you'd get a two dimensional pattern. In-between these two are various distorted ellipses. The software scans the waveforms looking for the time points where they cross their average value zero crossing with DC offset removed. Handbook for sound engineers 3 ed. They are closed shapes.

Lissajous figures are produced in two dimensions when the x and y coordinates are given by two sine waves, which may have any amplitude, frequency and phase. the constructive and destructive interference in one of the sound files below.

us to show the interaction of the two signals on a different way: usually with a. Lissajous figures tells us about the phase difference between the two signals and the ratio of 3: Two sine waves of equal frequency, 90 degrees out of phase. In physics and mathematics, the phase of a periodic function F {\displaystyle F} F of some real spanning a whole turn, one gets the phase shift, phase offset, or phase difference of G {\displaystyle G} G relative to F {\displaystyle .

Then the signals have opposite signs, and destructive interference occurs. When the phase.

In the old days of analogue Cathode Ray Oscilloscopes, this literally controlled the speed with which the electron trace passed from left to right of the the screen. A common example is the phase difference between the input signal and output signal after it passes through a circuit, cable, or PC board trace.

The bottom of the figure shows bars whose width represents the phase difference between the signals. The phase of an oscillation or signal refers to a sinusoidal function such as the following:.

### Destructive Interference COSMOS

For those old timers who have started out their careers using an analog oscilloscope, you probably remember using the classic Lissajous pattern to measure the phase difference of two sine waves. This often varies slightly from

Phasors, Interference, Beating Between Tones, and Lissajous Figures.

INTRODUCTION frequency, but different phases (or delays).) cos.) cos.)(2. 1 θ ω θ. A simple clock would produce a sawtooth wave (like this) that would To start with, Lissajous curves are useless if the frequencies are not However, there is no interference involved in the production of the lissajous pattern. can measure the current phase difference between various paths or sources.

In this figure, the waveform on channel A provides the horizontal or X displacement.

The amplitude of different harmonic components of same long-held note on the flute come into dominance at different points in the phase cycle.

## Department of Physics Lissajou Figures Durham University

Or, conversely, they may be periodic soundwaves created by two separate speakers from the same electrical signal, and recorded by a single microphone. The oscilloscope will display two sine signals, as shown in the graphic to the right. All periodic signals can be described in terms of amplitude and phase. In other projects Wikimedia Commons.

## Lissajous figures from Physclips

Lissajous figures phase difference for destructive interference |
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Figure 1 Time plot of two sine waves. The latter is much more stable, precise and the two outputs may be phaselocked. The two channels from the oscillator drive the two channels on the top machine, and the one below shows the interaction of the two signals. Lissajou figures are created by the combination of two sine waves. Phase comparison is a comparison of the phase of two waveforms, usually of the same nominal frequency. The large number of harmonics on its screen tells you that, for this photograph, we were using non-linear superposition. |

Categories : Wave mechanics Physical quantities. The large number of harmonics on its screen tells you that, for this photograph, we were using non-linear superposition.

For those old timers who have started out their careers using an analog oscilloscope, you probably remember using the classic Lissajous pattern to measure the phase difference of two sine waves.