Physics of Electronic Sound
Exam 2 Solutions - Winter, 2000

1.A bass reflex speaker enclosure has a port, or opening, in the enclosure, in order to use the rear wave of the speaker. Baffles increase the path of sound emanating from the enclosure to shift its phase with respect to the front wave. The port can be "tuned" by adjusting the size of the opening and its length, analogous to how a Helmholtz resonator is tuned. The net effect is to improve the overall speaker efficiency by using the rear wave. The main speaker resonance is shifted to lower frequency to provide better bass response, as well.

2. Series combination: 300 Ohms. Parallel combination: 100*200/[300] Ohms = 67 Ohms.

3. Power is proportional to voltage squared, so increasing the voltage by a factor of the square root of two, or 1.414, would double the power.

4. Refer to the filters lab for a sketch. The circuit would be a closed loop consisting of a function generator, resistor and capacitor, all in series. The output voltage would be the drop across the resistor. Cutoff is defined to by R = 1/[2fC], so C = 1/[2(1000 Hz)(1000 Ohms)] = 1.6x10-7 F.

5. Thick wires are used for speakers because the thicker the wire, the lower the resistance per unit length. Speakers typically have nominal resistances of 8 ohms or less, so if a long, thin wire were used to connect the speaker, there may be significant power loss in the wire itself.

6. Refer to the filters lab for a sketch. The circuit would be a closed loop of a function generator, resistor and inductor in series. The output voltage would be the drop across the resistor. Cutoff is defined by R = 2fL, so f = R/[2L] = 1000 Ohm/[2 0.25H] = 637 Hz.

7. An n-type semiconductor is formed when silicon, which has four valence electrons, is doped with a small percentage of arsenic, which has 5 valence electrons. The lattice is largely comprised of silicon, so only four electrons are needed for bonding. This allows the fifth electron of each arsenic atom to be relatively "free," i.e. able to conduct current. Diodes are comprised of the junction of a p-type and n-type semiconductor, while bipolar junction transistors may have one (pnp) or two (npn) n-type regions.

8. Refer the operational amplifier lab for a sketch of the circuit. The resistor to the inverting input should be 10 k, while the feedback resistor, connected from the output to the inverting input, must be 200 k for a gain of -20. The non-inverting input must be at "ground."

9. Total Harmonic Distortion, or THD, is defined as the ratio of the voltage of unwanted harmonics to the voltage of the desired fundamental. If a signal at 1 kHz is input to the amplifier, it may produce a small amount of harmonics at 2 kHz, 3 kHz, etc, and these would constitute the harmonic distortion. A level of less than 1% is typically not noticeable, and many amplifiers have THD of a few tenths of a percent or less. The level of THD will depend on how much power is drawn from the amplifier, generally increasing with the power level.

10. The sound coming out of the left speaker would be due to signals bleeding in from the right channel, and should be 40 dB softer. Each 10 dB corresponds to a doubling or halving of loudness, so the left speaker sound should be 24 times softer, or 16 times softer.

11. The loudness switch on a preamplifier, when turned on, boosts the very low and very high frequencies by a set amount. This switch is used when listening to music at a very soft level, in order to compensate for the way an average human hears, which is not very well at low and high frequencies when the overall sound level is low. At greater sound levels, human hearing has a somewhat "flatter" response, and the loudness switch can be turned off.

12. Amplifier B has the lower signal-to-noise, so it will generate more noise at a given output signal level. At a fixed level, the noise in B will be 20 dB greater, which corresponds to two doublings of loudness, 10 dB for each doubling. Hence, B's noise will be 4 times louder than A's.

13. Flat response in an amplifier means that the amplifier's gain is constant at all frequencies. Flat response is a good thing, since it means that the output signal will not be distorted with respect to the input signal, i.e. the representation of the input in the output will be "faithful."

14. Gain = [output voltage]/[input voltage] = 10/0.02 = 500. It is dimensionless.

15. See the text for a picture of a rectangular bar magnet. It should have a north and south pole at opposite ends, and the magnetic field lines should form closed loops, with the field direction pointing from north to south.

Bonus. The amplifier gain appears to be only 5, while the ratio of feedback to input resistors suggests it should be 10. Thus, the actual input to the amplifier is reduced by a factor of two due to the output impedance of the function generator, which must be equal to 200 .