## IV. Procedure: Fourier Analysis

Almost anyone with normal hearing can distinguish between the sound of a piano and a banjo, even when these instruments play the same note, say Middle C or 256 Hz. The characteristic differences arise from overtones;  that is, although the amplitude of the oscillation at the fundamental frequency might be the same in each case, the amplitude of the oscillations at various overtone frequencies will be different for each instrument. The process of resolving a complicated waveform into its sinusoidal components (in our musical example, the fundamental plus the overtones) is called Fourier analysis.

Your instructor will demonstrate how to use DataStudio with the Pasco interface and a sound sensor to look at the waveforms (Amplitude versus time) produced by various sources of sound or other devices. This program will also analyze your waveform and tell you the frequency distribution from which your waveform can be reconstructed (i.e., it will tell you the sinusoidal components of your complicated wave as Frequency versus time by doing a Fourier analysis). The Sound Analyzer in DataStudio will enable you to analyze the sound in both of these ways.  You can change scales for either graph by placing the cursor over the scales and dragging the arrow that will appear.

To guide you in learning about Fourier analysis, you should do the following:

1.  Display the waveform when you whistle into the microphone.  Change the pitch and watch what happens.

2.  Display and analyze the waveform from your speaker as it produces the 1000-Hz sinusoidal signal.

3.  Display and analyze the 1000-Hz square wave that is produced by the output signal within DataStudio.  Make sure to look at frequencies on the Amplitude versus frequency graph up to 10,000 Hz. Do you see a pattern?

4.  Display and analyze the waveform produced by a tuning fork.

5.  Display and analyze the waveform produced by your voice.

In each case, include a discussion of how the Fourier analysis graph is related to the amplitude versus time display.  Make sure your notebook contains a printout of your analysis; this includes both an amplitude vs. time graph and an amplitude vs. frequency graph for each case.  Make the graphs representative of the whole frequency range needed to represent the sound, not just a narrow part of it.