The Resonance “Machine”

A custom-made resonance machine (and simple sonic tube).

If the above photo looks unfamiliar it may be because the “Resonance Machine” is not a commercially produced product but a one-of-a–kind science teaching aid. The “pink snake” is a simple, fun, hand-held resonance demonstrator.

The term “resonance”, or reverberation, comes from the Latin: “re” to repeat , and “sonorum”, sound. This definition is helpful because it summarizes what happens when a stimulating sound or vibration is reinforced in some manner. It is different from an echo, which is a repeated sound with a delay caused by the time to travel to a distant point and travel back.

The key concept of resonance is the effect of a specific pitch or tone as it impacts an object, which has a natural “resonant” frequency matching the incoming sound. The classic, but infrequent example of the opera singer hitting a pure high note while standing near a glass goblet and the goblet beginning to reverberate and shatter has been demonstrated by Myth Busters and recorded on high speed film:

While this dramatic and difficult feat is rare, the occurrence of resonance in nature is common. A playground swing is a pendulum. All pendulums have a natural period or frequency. If you attempt to make a swing go faster or slower it will resist and return to its natural frequency. A piece of wood or metal will have a natural frequency dependent on its’ shape and hardness. A simple way to discover the resonant characteristics of the object is to strike it or drop it on a hard surface. It is easy to distinguish the sound of breaking glass from the sound of breaking wood.

A column of air (captured in a tube or pipe) has a natural frequency. In fact the acoustic qualities of air (79% Nitrogen, 21% Oxygen) are significantly different from Helium. Anyone who has inhaled a deep breath of Helium and immediately spoken or sang will sound like Donald Duck. All musical instruments depend on the resonant properties of their material and shape. A tuba, which is large, will have a much “deeper” voice than the much smaller flute. Stringed instruments such as the guitar have multiple strings, whose pitch can be adjusted by using a finger to hold a string to a fret and thus instantly change the length, and hence the tone. The result, of course, is the instrument can produce a wide range of musical notes.

The period, or length of time for one complete cycle, can be vastly different in different circumstances. The unusually high tides in the Bay of Fundy are partially attributed to the resonant characteristics of the Bay itself. The orbital path of planets is a form of resonance. The 365 day year of our Earth is a result of its orbital speed around the Sun. While the period of audible sound ranges from 20 cycles per second to 20 thousand cycles per second the period of radio and TV signals is many millions of times per second and light waves have an even much higher frequency, or shorter period. The amazing fact, however, is that despite the fact that at any moment the air around us is filled with the signals from dozens or thousands of stations and yet our electronic devices are easily capable of ignoring all but a single one that we might choose.

Perhaps the most amazing demonstration of resonance in found in our ears! Yes, the human ear, and many animal ears, have similar organs to receive and decode sounds. Found deep inside the human ear is a structure called the cochlea. Biology students should be familiar with it and its associated eardrum. The cochlea is a tiny coiled tube filled with a fluid and hundreds of tiny hairs arranged in ascending order of length much like of set of pipes in a pipe organ. Incoming sounds strike the eardrum stimulating it in unison with the sound waves. The tiny hammer and anvil connect the vibrations to the cochlea. The auditory nerve sends signals to the brain, which interprets the sounds. The key point here is that the base of each hair contains a nerve cell which when stimulated by the movement of the associated hair, in effect, is a selective receptor for a specific sound frequency. Understandably, the longer hairs respond to the lower tones and the shorter hairs to the higher tones. The delicacy of hearing is often unappreciated. Loud sounds for sustained periods can damage the delicate hairs. Unfortunately they do not grow back. The shorter ones tend to wear out first causing a hearing loss in the higher pitch sounds. Hearing “aids” can partially compensate for these losses.

Enter the Resonance Machine. Many vibrations in nature are invisible, or difficult to observe accurately. Even though our eyes may see a guitar string vibrate the human eye is not capable of distinguishing one note from another just by watching the vibrating string. Even harder to comprehend are the completely invisible radio or TV waves. The Resonance Machine was conceived and built to slow down and make visible the vibrations in a very understandable way.

Containing a set of 10 carefully tuned “reeds”, the machine has the capability of stimulating all of them simultaneously at a specific frequency that can be smoothly adjusted to cover the entire range of all 10! A small electric motor, a gearbox, a speed controller, and a battery combine to make this possible. As can be seen the reeds are all of a slightly different length and have a small wood weight at the top that can be adjusted to “tune” each reed. A typical demonstration begins with the motor off and manually touching several of the reeds to show how they behave. All of the reeds are mounted on a movable platform driven by the motor and gearbox.

The demonstration begins with the motor running at a slow speed and at a frequency lower than the longest reed. At this point all the reeds are moving in unison back and forth about a quarter of an inch. As the frequency is increased the longer reed begins to come alive and vibrate noticeably, but only an inch or two. As the motor speed is increased the platform speed increases and a point is reached that closely matches the resonate frequency of the reed. At this point the reed is swinging almost violently and the adjacent reed is now becoming alive. The speed progression continues and one by one as the resonate frequency of each reed is passed that reed not only comes alive but swings very actively. Finally, the platform is vibrating at a very high rate and all of the reeds now show only the small amount of travel present in the platform. The process can now be reversed with the speed gradually being slowed and each reed in turn becoming very active as its’ unique frequency is reached.

The pink snake is not a snake. It is an unusual interesting toy that coincidentally teaches about the principle of resonance. It is a hollow plastic tube with many small circular pleats. When the tube is pulled apart a popping sound is heard as each of the pleats folds or un-folds. If the user starts with the tube completely collapsed there will be several dozen “pops” by the time it is stretched to full length. The fun part is to listen to the changing sound with each successive pop. Starting with a fairly high pitch, by the end of the series the pops are noticeably lower in pitch. See the discussion section for the explanation.

Discussion: Resonance is a term that spills over from the scientific to the conversational. It is not uncommon for someone to remark: “That painting really resonates with me.” or “The speaker’s ideas resonated with the audience.” In the world of science the term is more specific. A piano tuner may not use the term but he/she will use a tuning fork (or electronic equivalent) as a standard for tuning a piano. The strings of the piano will be adjusted to resonate with the standard. An interesting side note (no pun intended) is that if any two frequencies are mixed there will be a resulting pair of new frequencies created: the difference between the two, and sum of the two. In other words, mixing a tone of 150 hertz (cycles per second) with a tone of 200 Hz will create two new tones of 50 Hz and 350 Hz.

Another fun fact about musical scales is that an octave increase will double the frequency. So Middle C (C4) has a frequency of 261.6 Hz and the next C, C5 will have a frequency of 523.2Hz. Played together they will have a very pleasing tone. Back to the piano tuner, in reality a tuning “fork” of 440 Hz, A4 is used as a starting point in tuning a piano. The science of piano tuning though fascinating, is beyond the scope of this lesson, requires a keen ear, and years of training.

In the early days of the invention of the radio the transmitters used a rotary spark-gap machine to produce the radio signal. These signals were a broad mixture of noise and static. The transmissions used Morse Code. If two stations were located near each other their signals would be indistinguishable. Improvement required pure signals and separate frequencies. With receivers that could be tuned to a single frequency both stations could operate simultaneously without interference. In effect the solution to the problem was to create an electronic circuit that had resonate properties. A thin slice quartz has a unique property know as the piezoelectric effect.

So, in addition to mechanical and acoustical resonance, there is electrical resonance that is the basis of all radio, TV, GPS, etc. transmitters. Depending on the thickness of the slice, the crystal it will support an electronic oscillation at one specific frequency. With crystal frequency control transmitters could send a signal on a single frequency. Today there are thousands of radio transmitters operating for commercial broadcast purposes and 2-way communication between aircraft, ships, vehicles, and even the International Space station. They do not interfere with each other. In addition blue-tooth devices, cell phones, garage door openers, GPS signals, wireless internet (WiFi) have become essential for the daily functions of commerce and personal devices.

The pink snake, shown in the top photo, although essentially a toy, is a simple demonstration of the acoustic properties of a pipe or tube. By stretching, the tube length is gradually increased with each “pop” of an expanding pleat. The secret is that each pop is not a pure tone, rather it is a fuzzy noise with many frequencies. As the length of the tube is increased the resonate frequency drops. Keep in mind that the principle of resonance is not simply a filter. Because each wave, or cycle, contains energy, the effect of the resonant chamber is to save the energy from each cycle and “grow” the resulting wave. The action is very similar to the person pushing a child on a playground swing. Each push does not have to be very hard because the energy of earlier pushes are still at work. Enough successive light pushes can accumulate and cause the swing to go quite high! Although the chamber is not exactly an echo chamber it behaves as a passive amplifier!

Notes: This is a “Learn More” section intended for the more curious or advanced student.

Three styles of typical resonance dampeners
found on power lines.

Although all of the above examples show important contributions that the principle of resonance provides to the natural world including our bodies, the resonance principle can have some un-wanted effects. In 1940 the newly constructed Tacoma Narrows Bridge was subject to 40 mph winds that set up oscillations in the main suspension span. After hours of violent oscillations the concrete and steel section failed and plunged into the water below. The occurrence is remembered in many physics books and influenced future bridge design. The cause of the oscillations was the resonance of the span caused by the “aeroelastic flutter” properties of the span.

Electrical power transmission lines can also be subject to high wind effects complicated by the natural resonance of the line itself much like a guitar string. Fortunately, devices have been created which “de-tune”, or dampen the vibrations of the wires.

Tall buildings can be damaged by earthquake vibrations. In effect a tall building has a resonant frequency which can be partially suppressed. By the use of large concrete blocks mounted on rollers in the top floors of buildings, the damaging swaying can be minimized.

taipei tower

Tuned mass dampers are widely used in production cars, typically on the crankshaft pulley to control torsional vibration and, more rarely, the bending modes of the crankshaft. They are also used on the driveline for gearwhine, and elsewhere for other noises or vibrations on the exhaust, body, suspension or anywhere else. Almost all modern cars will have one mass damper, some may have 10 or more.

The usual design of damper on the crankshaft consists of a thin band of rubber between the hub of the pulley and the outer rim. This design is often called a harmonic damper. An alternative design is the centrifugal pendulum absorber which is used to reduce the internal combustion engine‘s torsional vibrations on a few modern cars.