Sample questions to prepare for the final:

(quick answers here)

1. We've talked about singing in the shower and enjoying the resonances. Would this be affected by carpeting the shower?

2. My flute and my clarinet are about the same length, and yet the clarinet's range extends about an octave lower. Does this make sense?

3. All the strings on a guitar are the same length and  yet the open strings produce widely different frequencies - how can this be? And why is it that, while all the strings are the same length, they're not all the same thickness?

4. I know that to emphasize the fifth harmonic on a guitar string, I should lightly touch the string one fifth of the way from one end and then pluck the string. Amazingly, or not, when I measure the string and locate the point that's a fifth of the way from the end, I find a fret right there. Is this just a coincidence, or is it meaningful?

5. When I pluck that guitar string to excite the fifth harmonic, is there a completely wrong place to pluck it? Is there an ideal place?

6. Consider the clarinet family featured in Figure 3.9 in the textbook. Keeping in mind that the normal clarinet is the B-flat soprano, which is the second-smallest in the picture, approximately what is the lowest note playable on the biggest of these instruments?

7. If you pluck a guitar string very near the end, it sounds very twangy, and if you hit a drumhead very near the edge, it also sounds relatively high-pitched. Do these two similar phenomena have the same cause?

8. Sketch the fundamental mode and the next-lowest frequency mode of a clarinet, and then look at the location of the hole associated with the "octave key", which you open when you want to excite that next-lowest frequency. Where should this hole be, and why? Is it where it belongs?

9. Two speakers are connected to the same sine-wave generator. At one location (perhaps your ear) speaker A alone creates sound of intensity 1 microwatt per meter-squared. Speaker B alone creates sound of the same intensity. Now, if both speakers are on, the sound intensity could be different. What is the minimum intensity at this location, and what are the circumstances that could cause that to happen? What is the maximum intensity at this location, and what are the circumstances that could cause that to happen? Could the resulting intensity be 2 microwatts per meter-squared? If it's possible for the intensity to be different from that, where did the extra energy come from, or where did the missing energy go?

10. Suppose you hold down the sustain pedal on the piano, so none of the strings are damped, and you pluck the string for middle C. Of the strings within one octave of middle C, which will vibrate in response to this, and why?

11. Remember our 1m x 1m x 2m shower stall? Estimate the reverberation time in there, with you in there and without you in there.

12. Consider two humans singing harmony, with the interval between the notes being a major third, and let that be a perfect major third, so that the higher frequency is 1.25 times the lower.  If the lower note is A-4 (440 Hz), write down the all the frequencies that will be present, up to about the 6th harmonics. Which frequencies, if any, perfectly match? What happens if, instead of a perfect major third, the higher note is the D-sharp from the equal tempered scale?

13. Sometimes when you cut an instrument in half, its pitch rises by an octave, but on Monday we saw some cases where this is assuredly not true. Why is this sometimes true? Why was it not true for some of the instruments we saw on Monday?