1. Figures 1 and 2 are the polar plot of the sound radiation intensity given off by a vibrating diaphram in a wall, at various frequencies. what is the the relative intestity (relative to straight ahead) of the sound given off at 30 degrees for a frequency of twice the knee frequency? At 60 degrees? What are the relative intensities (compared to straight ahead) of the sound given off at 10 degrees and at 45 degrees for a frequency of eight times the knee frequency.
2. Deep sea divers can live underwater in a Helium-oxygen mixture, instead of air. (The nitrogen in the air dissolves in the blood under pressure, and is somewhat poisonous. It also comes out of solutions when the diver ascends, causing nitrogen bubbles in the blood, blocking the flow of blood- called the bends.) One diver likes to blow over coke bottles to annoy his mates. What would happen to the note that the bottle would produce in the helium-air mixture? Another diver brings down his guitar to use in the evenings. What effect would the different gas mixture have on his guitar? (Note that Helium-oxygen mixture is much lighter than air, although the compressibility is the same.)
3. Consider a clarinet with just one finger hole. What would you expect to happen to the note produced by that finger hole as the hole is made smaller and smaller?
4. Discussion:
The effect of the change in size of a tube on its resonances.
Given a tube fill of air ( either one end closed or not). If one changes the dimensions of the tube at some point, the modes and especially the frequencies of the modes will change. There is a law to how those frequencies change. If one widens [narrows] the tube at a point near where the pressure has an anti-node (i.e., has maximum oscillation and the velocity has a node) for a given mode, then the frequency of that mode will fall (rise). If one widens [narrows] the tube at a point where the mode has large velocity oscillations ( i.e., near the anti-node for the velocity, or node for the pressure), the frequency of the mode rises [falls]. Eg, for a coke bottle, one has narrowed the tube at the end where the velocity is high and pressure is near a node. The frequency of the fundamental ( and if fact of all of the modes) falls. Note that if one uniformly increases the diameter of the tube at all points by the same ratio, the two effects cancel, and the mode has the same frequency as before. (A wide pipe has the same resonant frequencies as a narrow tube to fist order.)
Question:
What is the dominant effect of the closed finger holes in a clarinet on the frequency of the lowest note of the clarinet? What is the effect of the bell at the end of the clarinet on the frequencies of the various modes? (remember that the walls of the clarinet, made of wood, have a substantial thickness).
5. What effect on the playing of a flute would the fact that it is made of gold or platinum rather than say plastic have?
6. a) We are back to our deep sea divers again. Some of the divers take down their clarinet, trumpet and flute. Assume that the velocity of sound in the helium-oxygen mixture is twice that of air. What will the effect be on these instruments? Why does the trumpet player have difficulty in playing his instrument? (Remember the relation between the lips and the note the trumpet player wants to play). How will the flautist have to adjust her playing style in this mixture?
b) What happens to the knee frequency of a given sized "speaker" in such a mixture?
7. Describe the similarities and differences between an oboe and a flute?
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