## 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 breaking 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 microphone to look at the waveforms (Scope in DataStudio) produced by various sources of sound or other devices (e.g., those wave patterns produced by your function generator). This program will also analyze your waveform and tell you the frequency distribution (FFT in DataStudio) from which your waveform can be reconstructed (i.e., it will tell you the sinusoidal components of your complicated wave). Thus you will be able to analyze the sound as both amplitude vs. time (scope) and amplitude vs. frequency (FFT). Note: the time and frequency scales for these two signal analyzers are connected. Changing the frequency scale on the FFT changes the time scale on the scope.

To guide you in learning about Fourier analysis, you should do the following (at a minimum):

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

2. Display and analyze the 1000 Hz square wave that is produced by your function generator and look at other frequencies up to 2000 Hz. Do you see a pattern?

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

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

In each case, make sure your notebook contains a sketch or printout of your analysis; this includes both amplitude vs. time (scope) graphs and amplitude vs. frequency (FFT) graphs.