I apologize for the roughness of these notes, as I have not had time to polish them (or even get rid of all typos).
> Have you got notes up on the web, though? I don't know anything about > what you've been teaching these last couple of weeks. The main thing I have been teaching is musical instruments-- woodwinds, trumpet, violin and voice. Three things are important. a) The amplifier feedback sound procduction. -- the key idea is that the feedback amplifier must be designed to increase whatever the effect in the instrument is. In the ordinary reeds, it is because in a certain range the reed closes as the pressure inide drops. This means that less air goes in when the pressure inside is low and more when it is high. This amplifies. What gets amplified is the mode in the instrument . For the lip reed ( trumpet family) it is the time delayin the reed. The trumpet reed opens as less pressure is inside. This would damp out any mode. However if you tune the reed ( your lips) to have their resonance just under the resonance of the mode, then the lips will have a greater than 90 degree lag wrt the driving force inside the instrument. Ie, they will open when the pressure in the instrument is high, and close when it is low. Again the air flow in is high when the pressure inside is high, and low when the pressure is low, which again amplifies. The flute (and beer bottle) , air reed, the operation is different. The oscillation of the air in the mode causes air to flow into and out of the instrument. the player directs a stream of air across the opening so that if there were no air flow in the instrument, about half would go in, and half out. Now, the mode air flow deflects the air stream from the mouth of the player. but it takes time for that deflection to affect how much of the air actually enters the instrument-- that air stream has to travel across the hole and to the other side. If this delay ( which is roughly the side of the hole divided by the velocity of the stream) is a quarter period, then the deflection, which occurs when the velocity of the mode at the mouth is max or min, will enter the instrument when the pressure is max or min. Again, a large air flow in when the pressure is high, will heighten the pressure, and a flow out when the pressure is low will lower the pressure more. Ie, again amplification. For a bow, the friction curve of the rosin on the bow plays the same role. The friction coefficient is high when the velocity is low and low when the velocity is high. Again this is a direct amplifier. If the velocity of the string wrt the bow (remember that the average velocity of the string wrt the bow is just the velocity of the bow) is lower than average, the friction force is higher, slowing it down even more. If the velocity is greater than the average, the friction force drops, allowing it to move even faster. The bow on the string enters this stick-slip regime, where the bow spends time sticking to the string and then breaking free. The velocity is a square wave with the duty cycle ( time spent sticking over time spent at high velocity) equal to the distance from the bow to the bridge vs the distance to the finger holding down the string. In the case of the pitch, in all the air instruments the pitch corresponds to the frequency of the particular mode that is being amplified. In a clarinet, the modes are the usual "closed tube" modes, with frequencies f1= c/4L (c=vel of sound, L=lengthof instrument) , f2=3f1, f3=5f1, ... Thus the sound coming out tends to be only the odd harmonics esp for the lower notes on the clarinet. The pitches are changed by a) shortening the length of the air column, (finger holes), and b) playing a higheri (second) mode ( going up in register) by opening the tiny register hole to damp out the lowest mode. In an oboe ( and bassoon, saxaphone), it is a conical bore instrument. Here the modes have frequencies of f1=c/2L, (ie an octave higher than for a clarinet ofthe same length), f2=2f1, f3=3f1,... The reed operates in the same way as for a clarinet. The modes however are different and thus the tuning of the second register is at only 2 the freq of the lower register (second mode is 2f1). Again the length is altered by finger holes. In a flute, the modes again have frequencies f1= c/2L, f2=2f1, f3=3f1 ( tube open at both ends). In a violin the frequency is determined by the mass of the string, the tension in the string, and the length. The mass and tension are set beforehand to tune the string to its standard frequencies ( G3 D4 A4 E5 on a violin, lower for the others-- eg viola is C3 G3 D4 A4). The pitch is changed either by choosing which string to bow, or by shortening the string by putting your finger down hard on the string. The next point is the transmission of sound out of the instrument-- how do the vibrations in the instrument get out as ssound. In the case of the wind instruments, it is fairly direct. The vibrations of the air in the instrument cause the air in the openings (end of tube, finger holes, blow hole of a flute) to vibrate back and forth. This acts like a speaker piston which then forces the air outside to vibrate creating sound waves. This translation ofthe piston motion to sound has the same efficiency problems that a speaker has-- ie the sound that gets out is 6dB per octave below the knee freq of the piston less than one would expect just due to the velocity of the piston (air) at the opening. The flaring of the trumpet say, does increase the diameter of the piston for the higher frequencies, making the efficiency greater, but does little for the lowest frequencies. In the woodwinds and flutes, since most of the air vibration occurs at the finger holes or at the mouthpiece (for a flute) the flaring plays very little role except for the lowest notes. In the violin the strings move essentially no air. Thus the body of the instrument. The bridge transmits the vibration of the string to the body by a lever action ( one foot of the bridge is held relatively static by the soundpost in the instrument. The bridge pivots around that foot, pushing up and down on the top). Of course the more massive the bridge, the less it moves, and the less the vibration is transmitted. The bridge also has its own resonances ( the bridge as a whole, or the top of the bridge rocking in opposite directions to the bottom) which tends to accentuate certain note ranges. The main sound production comes from the top and bottom of the instrument vibrating, and from the air in the f holes vibrating. Thus the resonances of the top plate (like a drum) and of the air inside the instrument with the f holes as openings will accentuate certain frequencies. The Helmholtz resonance is tuned to the D4, ( second lowest string) and the first of the drum modes is usually tuned around A4. the second drum mode is usually around E4 and then they start to crowd closer together. The motion of the string against the bridge is very much of a saw-wave pattern. But because of all of the resonances along the way, the sounds that come out of the violin have a very complicated spectrum which changes from note to note. For the voice, my main emphasis was on the incredible flexibility of the alterations of the vocal cavity ( throat mouth with tongue, teeth and lips) which alter the resonances of this cavity. The vocal chords vibrate due to a feedback mechanism (I hope to learn more in the colloquium this afternoon about what the exact mechanism is) but that sound it altered by the resonances of the vocal tract. Those resonances are called formants, and largely determine the vowel sound that is produced ( also some of the consonants-- the difference between thththt and sssss is the resonances produced at the front of the mouth in the vocal cavity by changes in the lips tongue and teeth.) I showed them the formant diagram showing how the first two formants ( resonances) primarily determine which vowel is heard and that the vowel sound is primarily determined by the location ofthose first two formants. I pointed out the singers problems-- When the voice sings at a certain pitch only the harmonics of that pitch are produced by the vocal chords. Thus the ear only has the intensity of the sound at those frequencies to use to determine where the formants lie. For a soprano, singing high, those harmonics are high in frequency and also widely spaced, making determination of the formant difficult. Also the singer wants a loud sound and so want to make sure that the vocal tract resonances lie on those harmonics, as otherwise the sound production will be poor and quiet. Thus sopranos tune the formants to the harmonics, rather than using the formants to sing a particular vowel sound. Ie, they mess around with the vowels in order to make a louder sound. Tenors (operatic) develop their throats to produce a strong third formant up at about 3KHz. This strengthens the sound at those frequencies, which is where the orchestra/choir is getting quieter. This allows teh tenor voice to "stick out" above the loudness of the orchestra/choir, even though on average the orchestra is much louder than the tenor is. This tenor's formant ( third resonance) is hard to develope, but is very effective.