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Oscilloscope and Frequencies

1. How can Lissajous patterns be used in checking out specific frequencies (such as in tuning a piano)?

2. What makes the sound of a violin different from that of a piano when they are playing the same note?

3. Can the wavelength of a signal be measured on an oscilloscope? Explain.

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The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Check out:
http://mathworld.wolfram.com/LissajousCurve.html
http://perso.wanadoo.fr/olivier.granier/meca/simul/lisajou/simul.html
http://en.wikipedia.org/wiki/Lissajous_figure

http://www.clubi.ie/amhiggins/adsr.html (where the ADSR figures were taken from)

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Usually in an oscilloscope, the input signal is a single wave, and the x-axis is the time while the y-axis is the amplitude of the signal.
However, a Lissajous' pattern is a result of two input sinusoidal signals. Then the x-axis is representing the amplitude of the first signal and the y-axis represents the amplitude of the second signal.

Where  is the relative phase difference between the signals.

When the frequencies are equal and the phase angle is zero we can see that:

Which is the equation of a straight line:

The slope of the pattern is the ratio between the amplitudes.

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Solution Summary

This solution is provided in 712 words in both a .doc and .pdf file attached. It discusses sinusoidal signals and includes equations and diagrams to further understanding of the problem.

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