Many people believe you can hear the ocean roar by putting a seashell up to your ear. True. Here's how: Hold the shell next to your ear and walk out into the surf until the water is over your head. You will definitely hear the ocean.
The muted "roar" you hear from the same shell on land, however, is something else altogether. It is the sound of trapped acoustic waves bouncing back and forth between the sealed end of the shell and its opening near your ear. The same effect occurs with other cylindrical objects, even with two open ends.
(The Horizon Test Center recommends two-inch-diameter plastic PVC pipe for this experiment. But cardboard tubes from rolls of toilet paper or paper towels will also work, as will soda bottles. To make the object behave the way a shell does, you should seal one end of the tube with tape or your hand. Leaving it open alters the pitch.)
Powering the sound waves are the random noises in the air around you -- the air conditioner, the refrigerator, the breeze or your neighbor mowing the lawn. Only a few of those vibrations become the "roar" you hear, the pitch of which is determined by the distinctive shape of the cylinder.
A chamber such as a seashell or our experimental tubes will resonate only to a particular set of waves: those that don't cancel themselves out as they bounce back and forth between the closed end of the shell or tube and the open end near your eardrum. These self-reinforcing patterns are called standing waves or resonances or harmonics.
These wave patterns depend on the length and shape of the tube. That's the main reason a flute makes a different sound than a clarinet, even though both are just pipes with holes in them.
Length is the key factor. For a shell or a closed-ended pipe, the resonant wavelengths turn out to be the odd fractions of four times the tube length. The longest standing wave that can form is one where the tube length is one-quarter of the wavelength. This is often called the fundamental wavelength or first harmonic.
For example, a one-foot tube (roughly the length of a paper-towel roll) with one end sealed will have a fundamental resonant wavelength of four feet. The next longest will be four feet divided by three (or 16 inches), then four feet divided by five (9.6 inches) and so on. These wavelengths are called overtones.
Now open the end of the tube and you'll hear a very different sound. That's because in an open-ended pipe, the longest standing wave is twice the length of the tube -- only half the length for a closed-ended pipe. So you'd expect to hear a pitch about an octave higher. Try it. It won't be as loud, but you should hear the change easily.
Open or closed, the longer the tube, the deeper the sound -- that is, the lower the pitch or frequency of the resonant waves. The scratchy "white noise" you hear is the fundamental plus all the overtones plus whatever random noise is around.
For extra credit, figure out what the lowest note is for your tube. The speed of sound in air is about 1,100 feet per second. (That's why you can tell how far away lightning is by counting seconds between the flash and the boom. Five seconds means about a mile.) And for a wave, the speed is equal to the wavelength times the frequency. For a six-inch-long closed tube, the fundamental wave is two feet long. That means the frequency is around 550 cycles per second. On a piano, that's about the same as the C above middle C. Check it out.
CAPTION: Air vibrating in a capped pipe moves fastest at the open end (an antinode) and is motionless at the closed end (a node). Because they have additional nodes, the overtones have shorter wavelengths and higher pitches than the fundamental. Shortening the pipe raises all the frequencies. (This graphic was not available)
SOURCE: Louis A. Bloomfield, University of Virginia