Introduction
In this experiment you'll measure two important parameters of a small loudspeaker enclosure, it's dispersion and frequency response.

Apparatus
Stanford Research DS345 synthesized function generator
Stanford Research SR760 FFT spectrum analyzer
Microphone
Creative CS120 speaker

What to do
In both sets of measurements, we'll use the FFT spectrum analyzer to measure the microphone signal as a function of frequency. In the first measurement, you'll find the speaker dispersion at two discrete frequencies, while in the second, a frequency sweep will allow a continuous recording of the speaker response.

1. Dispersion
Plug the speaker into the function generator and set the frequency to 200 Hz, adjusting the amplitude to a comfortable level that is not too loud. Hold the speaker in front of you and slowly rotate it by 90 degrees. Do the same for a 14,000 Hz signal, again adjusting the amplitude so it's not too overpowering. Again rotate by 90 degrees. Can you hear the effect of speaker dispersion? The speaker is enclosed, but estimate roughly what you think it's diameter probably is.

To test this phenomenon more quantitatively, mount the microphone about 25 cm or so from the speaker. Beginning "on axis," use the spectrum analyzer with the display on linear to record the voltage level of the 200 Hz tone. Rotate the speaker by 5 degrees and record the new peak voltage at 200 Hz. It may be advantageous to locate the front of the speaker over the edge of the table, to avoid complications due to sound reflection off the table top. Continue recording the signal amplitude every 5 degrees until the speaker axis is at a right angle to the microphone axis. Be sure to maintain the same distance between the microphone and the center of the speaker as you rotate, for the signal amplitude will drop with increasing distance between speaker and microphone.

Repeat the same procedure with the function generator at 14 kHz, recording a data set of microphone voltage vs. angle, every 5 degrees from 0 to 90.

2. Frequency Response
Starting with a 200 Hz sine wave, step the frequency up 10 Hz at a time until you reach 400 Hz. Can you hear any resonant behavior?

To record a quantitative spectrum of the frequency response, mount the microphone a few cm away from the speaker, and adjust the function generator to sweep from 200 Hz to 3100 Hz while the FFT analyzer records the spectrum. Useful settings to accomplish this are as follows: Set the sweep/modulate function to lin sweep (linear sweep...the frequency increases linearly with time), and to sawtooth. Adjust the start frequency to 200 Hz . The stop frequency can be set by first pressing the shift key, followed by the start key; set this to 3100 Hz, and press start again to enter. The sweep time is the inverse of the rate, which should be set to 0.01 Hz. Now press the sweep button, and listen...you should hear a tone whose pitch increases steadily in time, from 200 Hz to 3100 Hz over a time of 100 seconds.

Set the FFT analyzer to a span of 3.125 kHz, with a start frequency of 150 Hz. These settings will give you a background signal before and after the sweep of the function generator. The spectrum is a little more dramatic if the vertical scale is set to log. Now observe what happens when you sweep the frequency input to the speaker, with the microphone a few cm away. Can you follow the sweeping frequency?

To record a spectrum, press the average key on the FFT and set it to average 6300 traces. This number of averages should take about 100 seconds, to match the sweep time of the function generator. You can restart a sweep by turning the sweep key off and on again. Press the start button for averaging the FFT at the same time as you begin a sweep. A continuous spectrum of the microphone signal should appear. Print out a hard copy when you have a satisfactory spectrum. Using the marker key, measure and record on the spectrum the frequency of any outstanding peaks

Analysis
Plot your dispersion data on the polar coordinate graph paper provided. You may assume that the speaker's output is symmetric about its axis, so that you can plot from +90 degrees to -90 degrees using your data set. Attach the graph to a sheet of your lab notebook. Comment on the degree of dispersion at the two wavelengths.

Questions
1. What causes dispersion in speakers?

2. From your estimation of the speaker size, at what frequency would you expect dispersion to be significant? Does this agree with your measurements at 200 Hz and 14 kHz? Explain.

3. From the FFT frequency spectrum, what is the frequency of the main speaker resonance?

4. Are there any additional resonances seen in the FFT spectrum? What causes them?

5. There may be some non-idealities in the measurement techniques employed in this experiment. Comment on what you think these might be, and how one might overcome them, given materials and time to design an experiment.

Don't forget to include a purpose and a conclusion in your write-up.