Physics 104 Solutions
Symko, Chapter 4 - Loudspeakers

Questions for Review
1. Speaker enclosures are used to separate a driver's "rear sound" from its "front sound." The rear sound may be either absorbed, or delayed in order to put it in phase with the front sound. Efficiency and frequency response are two important parameters that are affected by the type of enclosure used.

2. A driver cone is a mechanical device that undergoes vibrations and has resonant frequencies, just like the surface of a drum. Ideally, the cone is stiff and doesn't flex as it pushes on air to create sound, but a real cone has resonant frequencies that cause ripples on its surface. This effect creates peaks and troughs in the frequency response of the driver, so the response is no longer flat, and this effects its ability to reproduce sound.

3. One driver can't be used for the whole audio range for a couple of reasons. First, there is the Doppler effect, where the movement of a source causes frequency shifts in the sound. A single driver would be moving slowly to reproduce low frequency sound, and if it was simultaneously generating high frequency sound, the latter would be shifted by the former. In general, small drivers are best for high frequencies, because they can respond quickly to rapidly oscillating electric signals, while large drivers are best for low frequencies, because a large volume of air must be moved to generate significant sound at low frequencies. Hence, a collection of drivers typically works best to handle the entire audio range.

4. A driver is not 100% efficient because anytime energy is transformed from one type (e.g. electromagnetic) into another (e.g. sound), there will be energy lost to heat or random motion.

5. Four basic speaker enclosures include the infinite baffle, the bass reflex port, the acoustic labyrinth, and the acoustic suspension enclosures.

The infinite baffle uses a large enclosure with sound absorbing material to negate the rear wave of the driver. It is thus large, cumbersome, and inefficient because half of its acoustic power is thrown away.

A bass reflex port allows the rear wave to emerge from the front of the enclosure after a delay, in order to create a reinforcing phase relationship with the front wave. The port opening or neck can be adjusted in cross sectional area or in length to tune the resonant frequency of the enclosure. The combination of rear and front waves generally creates a frequency response with two resonances. Standing waves inside the enclosure are reduced by adding sound absorbing material. In general, this type of enclosure is relatively small, efficient, and has a relatively flat frequency response that extends to low frequencies.

The acoustic labyrinth, or transmission line speaker, uses walls inside the enclosure to act as a "folded pipe" that largely absorbs the rear wave. It has a good frequency response but is not efficient.

Acoustic suspension enclosures are small and compact. Typically, a driver with a low resonant frequency is coupled to the small enclosure, which reduces the compliance significantly and raises the resonance to an appropriate frequency. The frequency response is generally good but the efficiency is very low.

6. A horn speaker is more efficient that a cone loudspeaker because it uses a small vibrating diaphragm that doesn't take much energy to vibrate, and the horn is a tapered structure that allows efficient coupling of the diaphragm's sound production to the room. When sound waves travel down a small cylindrical pipe that opens to a large room, the abrupt change in geometry causes significant reflection of the sound back down the tube. If the tube flares, though, more sound can be radiated out its open end. In general, a horn radiates high frequencies very effectively above the "cut-off frequency," which typically corresponds to a wavelength equal to four times the diameter of the horn.

7. Designing a loudspeaker involves many considerations, such as the desired efficiency, maximum power limit, room geometry and acoustics, desired size and type of listening. Most importantly, one needs to achieve flat frequency response to faithfully reproduce acoustic signals.

8. Dispersion arises because of the diffraction of waves. Low frequencies spread out in space more than mid-range frequencies, while high frequencies may be very directional. Diffraction is significant when the size of the vibrating membrane is comparable to the wavelength of the sound, or smaller.

9. Tweeters are small because they are not so massive and can therefore vibrate rapidly, to reproduce high frequency sound. Woofers are large because a large volume of air has to be moved to generate sound at low frequency.

10. A cross-over network sends an appropriate frequency range of audio signals to the appropriate speaker. For example, in a three-way speaker, high frequencies are sent to the tweeter, middle frequencies to the midrange driver, and low frequencies to the woofer.

Exercises
1. D. horn
2. B. there are three types of drivers in each enclosure, the woofer, midrange and tweeter
3. C. three
4. B. rarefaction
5. C. decrease
6. D. 118.75 Watts
7. C. very inefficient
8. B. separate the front-sound from the back-sound which has been produced by the diaphragm, especially at low frequencies
9. A. acoustic suspension
10. E. 225 Watts, 2.5%
11. C. the high frequencies
12. E. 4 times more than for X
13. B. decrease
14. B. the horn
15. D. tells how well the loudspeaker reproduces each frequency in relation to all others.
16. B. separate the sound into different frequency bands, and then send each band to the appropriate driver
17. C. maximum power rating
18. E. None of the above will necessarily give the best sound
19. A. 1600 Hz
20. B. a bass reflex speaker
21. A. 1376 Hz
22. D. equal amounts of sound will be sent to the woofer and to the tweeter
23. B. 172 Hz
24. A. increase
25. E. all of the above are correct
26. B. decrease, like the square root of the area
27. B. mixture of many frequencies such that the power is the same for each octave
28. D. it matches well the vibrations of a small diaphragm to those of a large volume of air
29. C. sensitivity
30. B. 1.5/12 = 12.5%