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Sequence 3-28 Standing waves in a tube of gas p25 POS2&3

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Tuning Forks

My interest in tuning forks was sparked a few years ago by an experience with the Ohm forks from the Acutonics system. It was amazing to experience the beautiful low frequencies of those forks zip through my body. I was already familiar with the wonderful sensations in the body from holding and playing my Tibetan singing bowl. Tuning forks are much more specific than a bowl. It is like comparing a laser beam to a shower. They both feel amazingly wonderful, but they have different purposes.

Since that experience, I have found that there are a wide variety of systems and ways of using tuning forks on the body. There are an infinite number of frequencies, so theoretically, there are an infinite number of tuning fork frequencies available.

We are beginning to understand that at the atomic level of matter, everything is in vibration. And that includes us. Sound is vibrational energy. It travels in a wave and pushes molecules around as it moves. It is useful to understand a little about how sound travels in order to understand how tuning forks work.

Sound moves at different speeds depending on what it is traveling through. Typically, the denser a material is, the faster sound moves through it because the molecules are closer together. In the air, sound moves at about 770 miles per hour. Sound moves through water about 4 times faster than through the air. It moves through steel, like railroad tracks, about 15 times faster than through the air.

Have you ever heard or read about aboriginal hunters who put their ears to the ground to hear where the animals are walking or running? That is because sound travels through the ground faster than it travels through the air.

Our bodies are about 80 percent water, so we can assume that a sound wave will move through the majority of our body at approximately the same speed sound travels through water. That is four times faster than through the air. Because our bones are denser than the soft material of the body, sound will move through our bones faster than through the soft tissue.

Tuning forks are made to sound at one specific frequency. For example, a tuning fork made to ring at 440 Hz is usually what musicians tune their instruments to. This frequency is standard for instruments so that all of the instruments in a group will sound harmonious when playing together.

Both of my sons learned how to play the recorder when they were in Grade 5. Listening to the class perform together was an exercise in tolerance and patience. If you have never played the recorder, they can be really out of tune if your blowing is too strong or too soft. Just imagine a class of 30 kids doing this all at once. Ouch for the ears, but important to encourage the kids. They were having fun. The parents were trying not to cringe.

A doctor will sometimes use a tuning fork to test whether or not a bone is broken. When a sounding fork is placed on the skin where the sound can travel through the bone, a patient will usually experience excruciating pain if the bone is broken.

Music therapist and naturopathic doctor, John Beaulieu spent over five hundred hours over two years in an anechoic chamber. With no stimulus or noise, he sat there listening to sounds of his own body. "He began to correlate different states of consciousness with different sounds of his nervous system. Being a trained musician he noticed that the high-pitched sounds of his nervous system consisted of several sounds in different intervals. Then one day he brought two tuning forks and tapped them. Immediately, he observed that the sound of his nervous system realigned to the sound of the tuning forks." (from an article called "Biosonic Repatterning" on John Beaulieu's website, www.biosonics.com.)

One set that I use pretty well every day is the perfect fifth tuning forks. This set consists of the musical note C tuned to 256 Hz, a frequency directly related to the frequency of the earth, and the musical note G tuned to 384 Hz creating the interval of a perfect fifth when they are played together. Research conducted by Dr. John Beaulieu, music therapist and naturopathic doctor and Dr. George Stefano, neurologist showed that these frequencies stimulated the production of nitric oxide in the body's cells within 30 seconds. Normal nitric oxide production is inhibited by stress and illness among other things. Here is a list of the physical benefits when your cells are producing and releasing nitric oxide.

Relief from stress, more energy and stamina.

The autonomic nervous system is balanced, better clarity of mind, less depression.

Nitric oxide strengthens the immune system.

Circulation is improved.

We have better digestion.

These two forks are available on our website as a set.

Tuning forks are like lasers. Some people say they are like surgical tools. Because of their precise frequencies they can have more precise effects. There is some fascinating research being conducted relating to frequencies and the human. I believe that tuning forks hold the potential for great precision as a healing tool.

Tuning forks are also available in several other kinds of sets. My own personal experience and research on tuning forks is still in progress, but I can share with you what I have learned so far. Tuning forks are available in single frequencies like the Om fork. My understanding of this frequency at the moment is that it is suitable for many general purposes, like calming or balancing. Some people may also experience specific physical or emotional effects from this fork.

The frequencies used in the set depend on the intention. For example, there are some that follow the musical scale: C, D, E, F, G, A and B or C, C#, D, D#, E, F, F#, G, G#, A, A#, and B. These sets follow the designation of corresponding frequencies to the chakras of the human being, mostly followed in the Western world. Please be aware though, that the musical note C is not fixed. What we call C is actually a wide range of frequencies close together. The musical note C on the piano, for example, is tuned to 261.626 Hz and is within the range of frequencies for C. Last month I discussed the perfect fifth set of forks with the fork for C tuned to 256 Hz. This is directly related to the frequency of the earth. Two sets of forks that follow the scale from C to B that I have found so far, are those created by John Beaulieu and Fabien Maman.

Another interesting set of forks is based on the mathematical principles of the Fibonacci series. A discussion of this series would take considerable time, so, if you are curious about the Fibonacci series, I will let you find out more on your own. From my understanding so far, this numerical sequence and the frequencies in the set follow universal law. Nature is abundant with this principle. When it is applied to sound in tuning forks it gives us a powerful physical reconnection to universal law and proportion.

One set I purchased a few years ago is based on triple number frequencies: 111 Hz, 222 Hz, 333 Hz, 444 Hz, 555 Hz, 666 Hz, 777 Hz, 888 Hz and 999 Hz. This set has some of the most balancing intervals for the human being. Yet they feel quite different from the C and G tuning forks mentioned previously. This set offers much to those who connect with numbers and numerology.

Another interesting set of tuning forks is called Holy Harmony and was produced by Jonathan Goldman and is based on frequencies from the bible discovered by Joseph Puleo and Leonard Horowitz. These frequencies are explained in the book, "Healing Codes for the Biological Apocalypse" by Puleo and Horowitz. Jonathan Goldman has created two CDs using this set of forks: "Holy Harmony" and "Waves of Light."

I have recently completed the first two levels in training as an Acutonics practitioner. This is a system of healing that uses tuning forks instead of needles on acupuncture points. It focuses on placing the forks on points of the meridian system of the body. The frequencies of these forks are derived from the harmonics of the orbits of the Earth, Moon, Sun and planets.

There are many more types of sets of tuning forks available. The above descriptions are those that I have found out about so far. If you would like information about obtaining any of the sets above, please contact us. I would also love to hear about any experiences you have had with tuning forks.

You can learn more about the different types of tuning forks. Click below for more information on them.
Otto Tuning Forks Chakra Tuning Forks

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My interest in tuning forks was sparked a few years ago by an experience with the Ohm forks from the Acutonics system. It was amazing to experience the beautiful low frequencies of those forks zip through my body. I was already familiar with the wonderful sensations in the body from holding and playing my Tibetan singing bowl.

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In order to make it easy to get started with the Application Builder, we included a few example applications in the Application Libraries of COMSOL Multiphysics version 5.0. This blog post will give you an overview of the Tuning Fork application and the structural vibration model that it is based on.

General Note on Tuning Forks

A tuning fork is used to calibrate instruments to a standard pitch. The most common standard pitch is 440 Hz for the note A. However, there are also other standards in use, frequently based on the note A. For example, the New York Philharmonic and the Boston Symphony Orchestra use 442 Hz and many orchestras in Europe use 443 Hz. You can buy tuning forks corresponding to all of these standards, but also tuning forks for other notes such as C, E, and G.

In addition to musical applications, there are industrial applications of tuning fork-like structures, such as in MEMS gyroscopes. The mechanism of vibration is similar in all these cases, so let's discuss that first.

Mechanical Vibrations

When you strike a tuning fork, it will vibrate in a complex motion pattern that mathematically can be described as the superposition of so-called resonant modes, or eigenmodes. Each mode is associated with a particular eigenfrequency and the combination of all eigenfrequencies creates the specific timbre that makes the characteristic sound of a tuning fork.

The higher eigenfrequencies correspond to resonant modes that will be dampened out more quickly than the lowest eigenfrequency of the so-called fundamental mode. Just a second or so after striking the fork, most of the higher modes are dampened out and all that can be heard is the sound of the fundamental mode as a clean tone. This is the pitch of the tuning fork.

The pictures below show the qualitative mode shapes of a few of the first eigenmodes. The deformations are exaggerated to show the shapes more clearly.

The fundamental mode has the prongs vibrate back and forth in a symmetric and balanced fashion, which transfers very little force to the handle. This mode is weakly dampened and sustained the longest after a strike. Many of the higher resonant modes have a twisting and rotational motion that transfer plenty of force to the handle and will be dampened out quickly by a hand holding it. The first balanced higher mode that, again, transfers very little force to the handle is at 2800 Hz and will sound together with the fundamental mode when striking the tuning fork.

A spectral analysis of a sounding tuning fork in real life indeed reveals this to be the case:

The pictures above correspond to a tuning fork that is constrained at the handle by someone holding it firmly. You get a slightly different set of modes in the case of a tuning fork that is unconstrained, such as if you hang it from a string. However, in both cases, the fundamental balanced mode is at 440 Hz.

As a side note (pun intended), the transient timbre of a tuning fork, including tonal contributions from the higher resonant modes, is what creates the characteristic sound of a Rhodes electric piano, which is essentially a collection of tuning forks, or tines, of different lengths.

Structural-Acoustic Interactions

In COMSOL Multiphysics, you cannot only simulate the vibration of the tuning fork, but also its coupling to the surrounding air domain and the resulting acoustic pressure wave. This capability is available in the Acoustics Module and is illustrated below.

This structural-acoustic model can be downloaded here.

The tuning fork application in the Application Libraries does not include the surrounding pressure wave, but is just a structural modal analysis. The core COMSOL Multiphysics product without any add-ons is sufficient to run this app.

Accessing Apps from the Application Libraries

The Tuning Fork app can be found in the Application Libraries, available from the File menu in the COMSOL Desktop user interface.

You may also download application files from the Model Gallery by signing into your COMSOL Access account. If a model in the Model Gallery also has an application associated with it, the file will appear with the extension .mphapp.

This particular application computes the fundamental frequency of an unconstrained tuning fork for a user-input prong length. Optionally, you can give the fundamental frequency as input and ask the application to find the corresponding prong length. This requires a simple optimization algorithm implemented in one of the methods contained in the application.

The app shown here is based on the Tuning Fork: Computing the Eigenfrequency and Eigenmode model, with minor modifications. The handle in the application is cylindrical, while in the other model example, it is slightly conical.

The Form Editor

Your app's user interface is created in the Form Editor and is streamlined with only a few outputs and user inputs:

Inputs:

Prong length or Target frequency

Sound duration

Outputs:

Frequency or Prong Length

Mode Shape visualization (normalized)

The Method Editor

The tuning fork application contains several methods, both local and global ones. A local method can be associated with a form object as indicated by a small icon in the lower right corner of the object. In this application, the objects having local methods are the three buttons for "Show Geometry", "Compute", and "Play Sound" as well as the check box "Find prong length".

These local methods handle basic user interface logic such as enabling and disabling the input field for "Prong length" based on the status of the "Find prong length" check box.

To open a local method in the method editor, use Ctrl+Alt+Click on the form object.

The most important global method is b_compute, which contains a secant method implementation for finding the prong length for a given frequency. The secant method requires a good starting guess and this is provided by an expression for the eigenfrequency vs. prong length relationship given by elementary beam theory. For more information on this beam theory expression, see the model documentation for the Tuning Fork model.

There is also a play_sound method that simply plays the fundamental frequency (with no overtones): playSound(fq, 1000*dur). The first argument to playSound is the frequency and the second argument is the sound duration in milliseconds. One could, of course, also perform a full transient simulation of the tuning fork as it is being struck, but this would require a lengthy computation and extensive processing of the results to find the fundamental frequency. Instead, the implemented modal analysis can be performed in less than a minute on a standard computer.

A method frequency computes the frequency for a given length and is called from the b_compute method.

The method set_results sets the results visualization and frequency output to be that of the seventh eigenmode in the list of found eigenfrequencies. The first six eigenmodes are referred to as rigid body eigenmodes and do not contribute to the sound of the tuning fork. They represent the six degrees of freedom of motion of a rigid body: translation in the three coordinate directions and three rotational angles. The seventh eigenmode corresponds to the fundamental vibrational frequency, which is true for any unconstrained object.

Further Reading

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In order to make it easy to get started with the Application Builder, we included a few example applications in the Application Libraries of COMSOL Multiphysics version 5.0. This blog post will give you an overview of the Tuning Fork application and the structural vibration model that it is based on.

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Sound: Sound, a mechanical disturbance from a state of equilibrium that propagates through an elastic material medium. A purely subjective, but unduly restrictive, definition of sound is also possible, as that which is perceived by the ear. Learn more about the properties and types of sound in this article.

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17 Vibrations and Sound-Real Worlds Physics

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Table chart sound pressure levels SPL level test normal voice sound levels pressure sound intensity ratio decibel comparison chart conversion of sound pressure to sound intensity noise sound units decibel level comparison of common sounds calculation compression rarefaction loudness decibel dB scale ratio factor unit examples - sengpielaudio Sengpiel Berlin

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dB table sound pressure levels SPL level test normal voice sound levels sound units decibel level common sounds sound intensity decibel comparison chart noise ratio Conversion of sound pressure to sound intensity calculation compression rarefaction loudness decibel dB scale ratio factor units - Eberhard Sengpiel sengpielaudio

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The Tuning Fork Mystery: unexpected vibrations

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Sound Fields Radiated by Simple Acoustic Sources

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Daniel A. Russell, Graduate Program in Acoustics, The Pennsylvania State University

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If you wish to relate middle C and semitones to your physics course use the free software here.

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If you wish to relate middle C and semitones to your physics course use the free software here.

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ChordWizard Products : Overview : Music Software

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The ChordWizard range of music software gives you the tools you need to explore, understand and compose great music. Connect yourself to the power of music theory in songwriting, improvisation and accompaniment, and experience the touch of pure creativity. Compare Products

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Two traveling waves which exist in the same medium will interfere with each other. If their amplitudes add, the interference is said to be constructive interference, and destructive interference if they are "out of phase" and subtract. Patterns of destructive and constructive interference may lead to "dead spots" and "live spots" in auditorium acoustics.

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Speed guns use Doppler radar to perform speed measurements.

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Speed guns use Doppler radar to perform speed measurements.

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A radar speed gun (also radar gun and speed gun) is a device used to measure the speed of moving objects. It is used in law-enforcement to measure the speed of moving vehicles and is often used in professional spectator sport, for things such as the measurement of bowling speeds in cricket, speed of pitched baseballs, athletes and tennis serves.

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Sound waves in a tube are guided acoustic waves and are 1d waves.

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Physics Site Links
Physics Home (p)
https://padlet.com/rdownes/p
Physics 6th year (py6)
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Real World Physics chapter by chapter
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Electricity Experiments
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The term harmonic has a precise meaning - that of an integer (whole number) multiple of the fundamental frequency of a vibrating object. The term overtone is used to refer to any resonant frequency above the fundamental frequency - an overtone may or may not be a harmonic.

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3rd overtone or fourth harmonic

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Play by clicking bottom right square (with arrow) and video will launch in vimeo website. Supports learning in Chap 16/17 of real world physics.

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Play by clicking bottom right square (with arrow) and video will launch in vimeo website. Supports learning in Chap 16/17 of real world physics.

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Important: A mistake was made in class. Open pipes and stretched strings allow all harmonics while for half-open pipe only odd ones can be formed.

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Important: A mistake was made in class. Open pipes and stretched strings allow all harmonics while for half-open pipe only odd ones can be formed.

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A three-minute video about multibeam and side scan sonar, including a visualization that shows how sonar data is used to make products like nautical charts. | Download: Soundscapes (75 MB)

Sonar, short for Sound Navigation and Ranging, is helpful for exploring and mapping the ocean because sound waves travel farther in the water than do radar and light waves. NOAA scientists primarily use sonar to develop nautical charts, locate underwater hazards to navigation, search for and map objects on the seafloor such as shipwrecks, and map the seafloor itself. There are two types of sonar-active and passive.

Active Sonar

Active sonar transducers emit an acoustic signal or pulse of sound into the water. If an object is in the path of the sound pulse, the sound bounces off the object and returns an "echo" to the sonar transducer. If the transducer is equipped with the ability to receive signals, it measures the strength of the signal. By determining the time between the emission of the sound pulse and its reception, the transducer can determine the range and orientation of the object.

Passive Sonar

Passive sonar systems are used primarily to detect noise from marine objects (such as submarines or ships) and marine animals like whales. Unlike active sonar, passive sonar does not emit its own signal, which is an advantage for military vessels that do not want to be found or for scientific missions that concentrate on quietly "listening" to the ocean. Rather, it only detects sound waves coming towards it. Passive sonar cannot measure the range of an object unless it is used in conjunction with other passive listening devices. Multiple passive sonar devices may allow for triangulation of a sound source.

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national oceanic and atmospheric administration

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Sonar, short for Sound Navigation and Ranging, is helpful for exploring and mapping the ocean because sound waves travel farther in the water than do radar and light waves. NOAA scientists primarily use sonar to develop nautical charts, locate underwater hazards to navigation, search for and map objects on the sea floor such as shipwrecks, and map the sea floor itself.

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The speed of sound is greater in hot air than it is in cold air. This is because the molecules of air are moving faster and the vibrations of the sound wave can therefore be transmitted faster. This means that when sound travels from hot air to cold air or from cold air to hot air it will refract.

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Ignore Young modulus and Bulk modulus parts