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# Oscilloscope and Frequencies

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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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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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Check out:
http://mathworld.wolfram.com/LissajousCurve.html
http://en.wikipedia.org/wiki/Lissajous_figure

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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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