Figure 5-45. What exotic components may we find inside this high-end audio component that’s used with a subwoofer to block high frequencies?
Figure 5-46. The black tape is removed, revealing a coil of magnet wire.
Figure 5-47. The audio crossover coil consists of a plastic spool and some wire. Nothing more.
So here’s the specification for this particular coil in an audio crossover network. Forty feet of 20-gauge copper magnet wire, wrapped in 200 turns around a spool of 1/16–inch-thick plastic with a hub measuring 7/8 inch in length between the flanges and 1/2-inch external diameter. Total retail cost of materials if purchased separately: probably about $1, assuming you can find or make a spool of the appropriate size.
Conclusion: there’s a lot of mystique attached to audio components. They are frequently overpriced, and you can make your own coil if you start with these parameters and adjust them to suit yourself.
Suppose you want to put some thumping bass speakers into your car. Could you build your own filter so that they only reproduce the low frequencies? Absolutely—you just need to wind a coil, adding more turns until it cuts as much of the high frequencies as you choose. Just make sure the wire is heavy enough so that it won’t overheat when you push 100 or more audio watts through it.
Here’s another project to think about: a color organ. You can tap into the output from your stereo and use filters to divide audio frequencies into three sections, each of which drives a separate set of colored LEDs. The red LEDs will flash in response to bass tones, yellow LEDs in response to the mid-range, and green LEDs in response to high frequencies (or whatever colors you prefer). You can put signal diodes in series with the LEDs to rectify the alternating current, and series resistors to limit the voltage across the LEDs to, say, 2.5 volts (when the music volume is turned all the way up). You’ll use your meter to check the current passing through each resistor, and multiply that number by the voltage drop across the resistor, to find the wattage that it’s handling, to make sure the resistor is capable of dissipating that much power without burning out.
Audio is a field offering all kinds of possibilities if you enjoy designing and building your own electronics.
Theory
Waveforms
If you blow across the top of a bottle, the mellow sound that you hear is caused by the air vibrating inside the bottle, and if you could see the pressure waves, they would have a distinctive profile.
If you could slow down time and draw a graph of the alternating voltage in any power outlet in your house, it would have the same profile.
If you could measure the speed of a pendulum swinging slowly to and fro in a vacuum, and draw a graph of the speed relative to time, once again it would have the same profile.
That profile is a sine wave, so called because you can derive it from basic trigonometry. In a right-angled triangle, the sine of an angle is found by dividing the length of the side opposite the angle by the length of the hypoteneuse (the sloping side of the triangle).
To make this simpler, imagine a ball on a string rotating around a center point, as shown in Figure 5-48. Ignore the force of gravity, the resistance of air, and other annoying variables. Just measure the vertical height of the ball and divide it by the length of the string, at regular instants of time, as the ball moves around the circular path at a constant speed. Plot the result as a graph, and there’s your sine wave, shown in Figure 5-49. Note that when the ball circles below its horizontal starting line, we consider its distance negative, so the sine wave becomes negative, too.
Why should this particular curve turn up in so many places and so many ways in nature? There are reasons for this rooted in physics, but I’ll leave you to dig into that topic if it interests you. Getting back to the subject of audio reproduction, what matters is this:
Any sound can be broken down into a mixture of sine waves of varying frequency and amplitude.
Or, conversely:
If you put together the right mix of audio sine waves, you can create any sound at all.
Suppose that there are two sounds playing simultaneously. Figure 5-50 shows one sound as a red curve, and the other as pale blue. When the two sounds travel either as pressure waves through air or as alternating electric currents through a wire, the amplitudes of the waves are added together to make the more complex curve, which is shown in black. Now try to imagine dozens or even hundreds of different frequencies being added together, and you have an idea of the complex waveform of a piece of music.
Figure 5-48. If a weight on the end of a string (length b, in the diagram) follows a circular path at a steady speed, the distance of the weight from a horizontal center line (length a, in the diagram) can be plotted as a graph relative to time. The graph will be a sine wave, so called because in basic trigonometry, the ratio of a/b is the sine of the angle between line b and the horizontal baseline, measured at the center of rotation. Sinewaves occur naturally in the world around us, especially in audio reproduction and alternating current.
Figure 5-49. This is what a “pure” sinewave looks like.
Figure 5-50. When two sinewaves are generated at the same time (for instance, by two musicians, each playing a flute), the combined sound creates a compound curve. The blue sinewave is twice the frequency of the red sinewave. The compound curve (black line) is the sum of the distances of the sinewaves from the baseline of the graph.
Theory
Waveforms (continued)
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