Quiz Solutions—Reviewing the Science of Audio
- Why are speaker drivers made in all different sizes?
Answer: High frequencies have a higher energy density (you have to move less air to produce the same amount of power). The amount of excursion needed for a given sound level is inversely proportional to the square of frequency, so producing a 100 Hz tone requires moving 100 times as much air as a 1 kHz tone. So low-frequency speakers need to be quite large. In contrast, tweeters are made small so that the problems of cone breakups and directivity are pushed outside the range of our hearing.
- What percentage of electrical power do the speakers you built convert into sound? Circle one:
- What's the difference between a capacitor and an inductor?
Answer: A capacitor accumulates charge to store energy in an electric field; you have to put a current into it to charge it up. An inductor accumulates current to store energy in a magnetic field: applying a voltage causes the current to change. As a consequence of this, an inductor's impedance is proportional to frequency (ZL = iωL) and a capacitor's is inversely proportional (ZC = 1/iωC).
- Why do speakers without closed enclosures have so much less bass?
Answer: The rear wave is out of phase with the front wave, and when the wavelength is large relative to the path length difference, they tend to cancel out.
- Why can you build speakers much better than commercial ones for the same cost?
Answer: In most commercial speaker systems, 30-50% of the price goes into profit and the majority of the rest is labor (building the boxes). That's why our speakers using $60 of components might be as good as speakers you can buy for $300 or more.
- Why are tweeters often offset from the centerline of a baffle?
Answer: When sound travels outward from the tweeter along the baffle, it reaches the edge and is re-radiated in all directions (diffracted). The diffracted sounds interfere with the sound direct from the tweeter. By making the baffle asymmetrical, you spread out those interference effects across a wider range of frequencies (making them less obvious).
- Would you have more or less need to do that with a highly directional horn tweeter?
Answer: There would be less need for offset tweeters if they were directional, because less sound would travel sideways along the baffle.
- When you put two drivers in parallel, their impedance decreases by half and sensitivity doubles (+6 dB). If you had a crossover designed for a particular tweeter and woofer, what would you have to do to the crossover if you were to put a second woofer in parallel? (Speaker manufacturers commonly have similar crossovers like this for different speakers in any given model line.)
Answer: You would have to change the tweeter L-pad to boost its level by 6 dB. In the woofer network you'd have to halve all inductances and double all capacitances, so that everything had half as much impedance as before (to match the halving of driver impedance).