# Exams

## Quiz Solutions—Reviewing the Science of Audio

1. 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.
2. What percentage of electrical power do the speakers you built convert into sound? Circle one:
3. 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).
4. 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.
5. 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.
6. 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).
7. 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.
8. 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).