At left in the photograph above is an organ pipe fitted with a sliding piston, in the middle is a glass bottle, and at right is a corrugated sound pipe. Near the center of the photograph is a plastic tube with a plastic fitting on the free end. The other end goes to an air line. To play the organ pipe, insert the fitting into the end of the rubber tube extending from the whistle end of the pipe, and open the valve on the air line to provide a gentle flow. You can play the organ pipe over a range where the piston is just inserted into the end, up to an octave and a fifth above that (vide infra). You can play the bottle, either by blowing across the top, or by using the air line with suitable flow. Though it might take a bit of practice, blowing over the top may be easier than using the hose. For the corrugated sound pipe, grasp it at one end and whirl the other around in a circle. The faster you whirl it, the higher the pitch of the harmonic you get. If you place the stationary end of the tube over the styrofoam peanuts, they will be carried into the tube by the airflow. Please see the notes below regarding all of these instruments.
The vibrating medium in all wind instruments is an air column, which in the instruments shown above, is set vibrating by means of turbulence created at one end of the instrument, or, in the case of the sound pipe, along its length. (In other instruments, such excitation is accomplished by continuously starting and stopping the airflow at a high frequency, either with a reed (single reeds, as in clarinets and saxophones, or double reeds, as in oboes and bassoons), or by buzzing of the lips (as in all brass instruments).)
At the end of the organ pipe to which the hose is attached, is a whistle – a small opening across the width of the pipe, in front of which is a knife edge. That is, the outside wall of the pipe is cut so that behind the opening, it forms a narrow wedge. This arrangement disturbs the streamlines of the air as it flows by, creating turbulence, which causes the pressure there to fluctuate, in turn creating a pressure wave throughout the length of the organ pipe. Since the pipe is open at the whistle, but closed at the piston end, only those frequencies for which the distance between the piston and the whistle equals one-quarter wavelength or an odd multiple of one-quarter wavelength, can survive in the pipe. (See demonstration 44.36 – Speaker over water-filled tube.) Unless you set the air flow too high, what you hear should be the fundamental. The lowest pitch available on this pipe (slide almost all the way out) is the C one octave below middle C (so about 130.8 Hz), and you can slide the piston in until you get the G above middle C (~392.0 Hz). The piston is marked up to the C an octave above middle C (523.3 Hz), but above the G below that, the behavior of the pipe becomes a bit strange. This is probably because the length of the pipe is now getting too close to its cross-sectional dimension, and transverse modes are now being excited.
The bottle in the middle of the photograph is something called a Helmholtz oscillator, or Helmholtz resonator. If you blow across the opening of any bottle, or other closed vessel that has some kind of neck at the opening, it behaves as a Helmholtz oscillator. As noted above, you can use the hose to blow compressed air across the mouth of the bottle, or you can blow across it with your mouth. If you blow with the right speed, at the right angle, you should be able to get a clear tone, at a frequency of about 192 Hz, which is a few Hz below the G below middle C. A second, similar, bottle is available, which blows at about 195 Hz. When you blow across the opening of one of these bottles, the lip of the bottle, in similar fashion to the whistle in the organ pipe, disturbs the streamlines of the air flow and creates turbulence, which causes the pressure inside the bottle to fluctuate. Because the volume of the neck is much smaller than the volume of the bottle itself, the motion of the gas that results from a fluctuation in pressure is smaller in the neck than in the rest of the bottle, and the gas within the neck of the bottle moves together, essentially, as a plug, compressing the gas below it in the main volume of the bottle. Together, the gas in the neck and the gas in the bottle act as a sort of mass-spring system, with the plug of gas in the neck behaving as a mass pressing down on the gas in the bottle. The gas in the bottle, so compressed, acts as a compressed spring, and, in relaxing, forces the gas in the neck of the bottle back up. This cycle repeats itself as the pressure fluctuations at the mouth of the bottle alternately force the gas in the neck down, and then allow it to spring back up. The formula for the oscillating frequency of such a system, which you can see here, is f = (v/2π)√(A/Vl), where v is the speed of sound in air (which equals √(γRT/M), where γ is the heat capacity ratio, CP/CV, R is the universal gas constant, T is the temperature (in Kelvins), and M is the molecular mass of the gas), A is the cross-sectional area of the neck, V is the volume of the bottle, and l is the length of the neck. You can see a derivation of this formula here, and a brief description of cavity resonance and cavity oscillations here. For the bottle shown, the inside diameter of the neck is 2.5 cm, for an area of 4.9 cm2, the length of the neck is 3.0 cm, and the volume of the bottle (not including the neck) is 770 ml. Because of the way the air column in the neck couples to the air in the bottle and the air outside the opening, there are two corrections to the neck length, which are given in the web page above that has the derivation of the formula. These are to add 0.6 neck radii at the outside opening, and one neck radius at the inside end. This makes the effective neck length for our bottle (3.3 + 0.75 + 1.25) = 5.3 cm. Inserting the dimensions of the bottle, and 34,600 cm/s for the speed of sound, into the equation gives a resonating frequency of 191 Hz.
The corrugated sound pipe at right also takes advantage of the phenomenon of turbulence. As you whirl one end of the tube around, the airflow across the whirling end lowers the static pressure there. (See demonstration 36.75 -- Suck “peanuts” up pipe, and related demos.) In addition, because the air near the end of the tube is going around in a circle, a radial inward force is necessary to hold the air in the tube. (See demonstration 16.06 -- Twirl ball(s) on string.) Since the end of the tube is open, there is nothing to provide this force, and the air flows out through the end of the tube. Thus, as you twirl the pipe, air flows through it from the bottom to the top. As it does so, the air near the wall of the pipe encounters the corrugations, which, by disrupting the flow along the wall through viscous drag, create turbulence along the length of the pipe, which in turn causes pressure fluctuations in the column of air in the pipe. Since the pipe is open at both ends, there is an antinode at each end, and only those frequencies for which the length of the pipe corresponds to an integral number of half wavelengths, survive. (See demonstration 44.33 -- Speaker over pipes.) The faster you twirl the pipe, the greater the speed of the air through it, and the higher the frequency of the harmonic that you hear.
Important note: Ideally, as you begin to twirl the sound pipe, the first pitch you should hear should be the fundamental, then, as you increase the speed, the second harmonic, third harmonic, etc. Because of the stiffness of the pipe, it is difficult to swing it slowly enough and still get sufficient airflow to sound the fundamental. You can get hints of it, but it is virtually impossible to sustain. If you blow across the end of the pipe, though, you can get it to sound. You can tell that this is so, because the first clear tone you get is about 410 Hz (just shy of the A-flat above middle C, which is 415 Hz), and the second pitch you get is a perfect fifth above this (about 615 Hz, just below the E-flat above the C an octave above middle C, which is 622 Hz). If the lower pitch were actually the fundamental, the next higher pitch you would hear is the octave above it (820 Hz, just shy of the A-flat at 830 Hz). Since this next pitch is at an interval less than an octave above the first pitch, the first one cannot be the fundamental. That it is a perfect fifth, which corresponds to a frequency ratio of 3:2, tells us that the lower pitch is actually the second harmonic, and the higher pitch is the third harmonic. You should be able to get the second, third, fourth and fifth harmonics. Relative to the frequency of the fundamental, their frequencies are, respectively 2:1, 3:1, 4:1 and 5:1, and their distances above the fundamental are, respectively, an octave, an octave plus a perfect fifth, two octaves, and two octaves plus a major third. The spacings between neighboring harmonics (not including the fundamental) are: 3:2 – a perfect fifth, 4:3 – a perfect fourth, and 5:4 – a major third.