. I'm a musician seeking to better understand harmonics. I've read plenty of definitions and so I understand "what" they are, but I'm having a hard time visualizing them. What confuses me is the idea that a string can vibrate at multiple frequencies at once, that it can support multiple standing waves. How could a string bend in so many different ways at the same time? thanks!! — K, Mountain View, California
To help you visualize how a string can vibrate at several frequencies at once, I wrote a flash program that shows you what a vibrating string looks like. That program should appear below this note. It allows you to adjust eight parameters: the amplitudes of the string's four simplest vibrational modes (its fundamental vibration through its fourth harmonic vibration) and the phases of those modes. The program starts with a pure fundamental vibration of the string, which is easy to visualize. But you can turn on the second, third, and fourth harmonic vibrations to whatever extent you like. What you'll observe is that a string that's vibrating at several frequencies at once has a complicated shape, but doesn't look all that unfamiliar. It's simply a mixture of several standing waves that evolve at different rates. As a result, it exhibits a fancy rippling shape that you've probably see on a jump rope or a clothesline.
If you look carefully at the string while it's vibrating in a mixture of several harmonics, you'll see that it has only one shape at any moment in time. It's just a jiggling string, after all. The parts of that shape, however, are evolving at different rates in time and those parts are actually the different harmonics going through their individual motions at their own frequencies.
. Ever since someone struck and damaged the rear bumper of my SAAB 9-3, the air pressure inside the car has been unbearable to myself and passengers. It causes ear pain and nausea after around 15 minutes of driving. The only solution is to open the windows. Can you think of any structural aspect that may cause a problem like this? - TA
I suspect that the air inside the car is vibrating the way it does inside an organ pipe or in a soda bottle when you blow carefully across the bottle's lip. This resonant effect is common in cars when one rear passenger window is opened slightly. In that case, air blowing across the opening in the window is easily deflected into or out of the opening and drives the air in the passenger compartment into vigorous vibration. In short, the car is acting like a giant whistle and because of its enormous size, its pitch is too low for you to hear. Instead, you feel the vibration as a sickening pulsation in the air pressure.
For the one-open-window problem, the solution is simple: open another window. That shifts the resonant frequency of the car's air and also helps to dampen the vibrations. Alternatively, you can close the opened window. In your case, the resonance appears to involve a less visible opening into the car, perhaps near the rear bumper. If you can close that leak, you may be able to stop the airflow from driving the air in the car into resonance. If you are unable to find the leak, your best bet is to do exactly what you've done: open another window.
. How do the automatic doors at a supermarket know when to open and close? How do they work? — KL
Devices that sense your presence are either bouncing some wave off you or they are passively detecting waves that you emit or reflect. The wave-bouncing detectors emit high frequency (ultrasonic) sound waves or radio waves and then look for reflections. If they detect changes in the intensity or frequency pattern of the reflected waves, they know that something has moved nearby and open the door. The passive detectors look for changes in the infrared or visible light patterns reaching a detector and open the door when they detect such changes.
. Is there sound in space? If so, what is the speed of sound there? — MH
No, there is no sound in space. That's because sound has to travel as a vibration in some material such as air or water or even stone. Since space is essentially empty, it cannot carry sound, at least not the sorts of sound that we are used to.
. I would like to make high frequency and ultrasonic whistles with tubes. I know the formula for the relationship between wavelength, speed, and frequency but what is the relationship of these quantities with tube length and diameter? — AH, Richmond, British Columbia
If a whistle's tube is relatively narrow, its pitch is determined primarily by its length and by how many of its ends are open to the air. That's because as you blow the whistle, a "standing" sound wave forms inside it—the same sound wave that you hear as it "leaks" out of the whistle. If the whistle is open at both ends, almost half a wavelength of this standing sound wave will fit inside the tube. Since a sound's wavelength times its frequency must equal the speed of sound (331 meters per second or 1086 feet per second), a double-open whistle's pitch is approximately the speed of sound divided by twice its length. For example, a whistle that's 0.85 centimeters long can hold one wavelength of a sound with a frequency near 19,500 cycles per second—at the upper threshold of hearing for a young person. If the whistle is closed at one end, the air inside it vibrates somewhat different; only a quarter of a wavelength of the standing sound wave will fit inside the tube. In that case, its pitch is approximately the speed of sound divided by four times its length. However, if you blow a whistle hard enough, you can cause more wavelengths of a standing sound wave to fit inside it. A strongly blown double-open whistle can house any half-integer number of wavelengths (1/2, 1, 3/2, or more), emitting higher pitched tones as it does so. A strongly blown single-open whistle can house any odd quarter-integer number of wavelengths (1/4, 3/4, 5/4, or more).
. Is it true that you can determine the distance of a lightning bolt by counting the second that are between the sound of the thunder and the flash of the light? I heard that every second represents one mile in distance. — LS, Los Gatos, CA
You can tell how far away a lightning flash is by counting the time separating the flash from the thunderclap. Every five seconds is about a mile. The reason that this technique works is that light and sound travel at very different speeds. The light and sound are created simultaneously, but the light travels much faster than the sound. You see the flash almost immediately after it actually occurs, but the thunderclap takes time to reach your ears. You can determine how long it takes sound to travel from the lightning bolt to your ears by counting the seconds between the flash and the thunderclap. Since it takes sound about 5 seconds to travel a mile, you can determine the distance to the lightning bolt in miles by dividing the seconds of sound delay by 5.
. How does an ultrasonic bath work? — PT
An ultrasonic cleaner exposes a bath of liquid to very intense, very high frequency sound. Sound itself consists of regions of high and low pressure that move through a material as waves. As these waves pass through the liquid in the bath, each tiny portion of liquid vibrates back and forth in response to these pressure fluctuations. Near the surface of an object immersed in the bath, the liquid is pushed first toward the object and then away from it. The pressures involved are large and the changes in velocity within the liquid are so intense that occasionally the liquid will actually pull away completely from the object so that a tiny empty cavity forms. In effect, the liquid is jumping up and down on the object's surface and it occasionally jumps so hard that it leaves the surface altogether. Cavities of this sort are unstable and the liquid soon returns to the object. When it does return, the liquid collides violently with the surface and the liquid's pressure skyrockets as it transfers all of its momentum to the object in millionths of a second. This "cavitation" process is what cleans objects immersed in the ultrasonic bath—the dirt and grime are pounded free by the liquid when it returns to fill cavities that have formed during the vibrations.
. How can you demonstrate that sounds are waves produced by the vibration of material objects? — TP, Huntington Park, California
I can't think of an easy way to make sound waves visible while they travel through air, but it's relatively easy to make sound waves visible as they travel through materials. If you choose a system in which the sound waves bounce back and forth many times through a material, you can sometimes see the sound waves as they move. For example, partially fill a crystal wine glass with water and then rub your wet finger gently around the rim of the glass. With some practice, you'll be able to get the wine glass to emit a pure tone as your finger alternately sticks and slips its way around the glass rim. As this tone appears—the vibration of the crystal glass itself—the water will begin to exhibit beautiful ripple patterns. You should be able to see these ripples by looking at a bright light reflected from the water's surface. The ripples are sound waves that are travel through the water, back and forth, as the glass vibrates.
Another system that makes the movement of waves visible is a stiff, thin aluminum plate that's supported rigidly and horizontally at only one point. If you sprinkle fine sand lightly over the surface of this plate and then bow its edge with a violin bow, it will begin vibrating with a clear tone. As it vibrates, the sand will drift into places where there is very little surface motion—the nodes of the vibrating surface. Once again, sound waves are traveling back and forth across this surface and the up-down motions squeeze the sand into certain parts of the plate. In this case, the surface's vibrations and the sound waves in that surface are the same thing—in example of the fact that vibrations and sound waves are intimately related and are in many respects exactly the same thing.
. How does a siren work? — MM, Waterloo, Iowa
A siren uses a perforated disk or drum to alternately block and unblock a stream of air. The classic siren has a spinning disk with a pattern of holes around its periphery. This disk is spun in front of a jet of air, producing pressure pulses that we hear as sound. A more modern siren has a spinning centrifugal fan that propels air radially outward through a pattern of holes in a drum around the fan. This centrifugal siren is much louder than the disc siren because the centrifugal system pushes large pulses of air through many openings at once, whereas the disc siren only has one pulsed source of air.
. How does a steam whistle work? — DR
As far as I know, a steam whistle is just a whistle that's blown by steam rather than air. The principle behind a whistle is straightforward: the air inside the whistle is driven into intense vibration by the stream of gas blown across a slot-shaped opening. This stream of gas is directed at the sharp edge on the far side of the opening and might or might not actually enter the whistle. If air happens to be flowing out of the slot-shaped opening as the stream flows across the slot, the outgoing air will deflect the stream outward and that stream won't enter the whistle. But if air happens to be flowing into the slot as the stream crosses the slot, the stream will be deflected into the whistle. This situation leads to an amplifying effect: if any air is flowing into the slot, the whole stream of gas will flow into the slot. If any air is flowing out of the slot, the whole stream of gas will flow out of the slot.
Now air inside the whistle is never perfectly still—it's always sloshing back and forth at least a tiny bit, much like water sloshes in a basin. As a result, there is always a little motion of air in or out of the slot. When the stream of gas begins to blow across the slot, it amplifies any tiny motions of air inside the whistle so that they become more and more vigorous. Soon the air inside the whistle is vibrating intensely and the resulting pressure fluctuations radiate outward from the whistle as sound.
This same principle is active in many other musical devices, including pipe organs and flutes. In a steam whistle, the stream of gas that drives this vibration is steam rather than air. Water is heated in a boiler until it forms moderately high-pressure steam and then the steam is released through a valve to a large whistle, which sounds loudly.