Music is the pleasure the human soul experiences from counting without being aware that it is counting. Gottfried Leibniz

Physics is the study of the physical world around us. That physical world is in constant vibration and those vibrations impinge on our bodies continually. Occasionally, the vibrator is in contact with the bodies directly. But more often, the vibrator sets in motion some medium that comes in contact with us. That medium is usually air and the phenomenon is called sound. While we have developed specially adapted organs (ears) that receive these vibrations and send data to the brain for interpretation, one can feel sound waves all over one's body. (See:surviving a rock concert.) Let us consider a brief investigation of sound.

We believe that sound is a wave phenomenon because it exhibits those properties that define waves. We define a wave to be a disturbance in a medium that carries energy through the medium without any gross migration of the medium.

Waves

--have a source
--need a medium for transport
--have a characteristic speed in a medium
--exhibit reflection, refraction, interference, & diffraction

There are three kinds of waves

1. Longitudinal waves - the displacement of the medium is in the same direction as the direction of propagation. A row of dominoes standing on edge can support a pulse passing through it if the first tile is pushed parallel to the row. Pushing perpendicular to the row yields nothing exciting. We believe that sound propagating through the air is longitudinal wave phenomenon. in that context, sound waves are mechanical. They rely on physical contact between the particles. As in the row of dominoes cited above, the first was moved slightly to touch the second, the second touches the third and so forth. It should be noted that while the surrounding air carries waves that are longitudinal, the source of those waves may be vibrating according to one of the other modes listed below. see the applet at
http://www.explorescience.com/activities/Activity_page.cfm?ActivityID=50

2. Transverse waves - the displacement of the wave is at right angles to the direction of propagation. A stadium wave is transverse. other example include waves on a string,waves on the surface of water; we believe that light is also transverse. You may wish to revisit our consideration of light as a wave.)

3. Torsional waves - this wave has a displacement at right angles to the other two directions cited above. This motion involves twisting and is exhibited in the Tacoma Narrows Bridge collapse.

What is a wave? See
http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html

wavelength - the straight line distance between crests in a transverse wave or between compressions in a longitudinal wave. Wavelength is usually denoted by the Greek letter (lambda).Wavelength is measured in conventional distance units.While wavelengths can vary over a wide range of values, common musical notes have a wavelength of the order of one meter

frequency - the number of waves emitted or received per unit time. The SI unit for frequency is the Hertz which is equivalent to 1/second. The range of audible frequencies for most humans is 20Hz to 20,000 Hz.

velocity of propagation - the speed of the wave. For sound in air, v = 300 m/s (approx.)

These quantities are related by the equation V = f (lambda)

http://www.kettering.edu/~drussell/Demos/reflect/reflect.html

http://www.kettering.edu/~drussell/Demos/refract/refract.html

http://www.cbu.edu/~jvarrian/applets/waves1/lontra_g.htm

http://www.mcasco.com/p1mw.html
http://www.physicsclassroom.com/Class/sound/soundtoc.html

Doppler effect

A loud speaker producing a continuous tone sends out into the carrying medium a series of compressions and rarefactions that are the essence of the sound. The compressions are a uniform distance apart as they leave the source and they travel in all directions at the speed of sound. At some distant point, a stationary receiver will note the arrival of the compressions at the same rate at which they were produced. This description is hardly cause for celebration.
But what if the source is moving toward the receiver as it makes its sounds? The result should show that the compressions are closer together. For any wave we know v = f l. If v = constant at any given temperature, the a smaller the wavelength, the larger the frequency. This change in frequency of a wave train due to the motion of the source, or the receiver, or both is known as the
Doppler effect. Think of the sound made by a car as it races by you. The car is making the same sound as it whizzes by. The difference you hear is one of frequency due to the fact that the source is moving.

Let us consider a simple analogy: You and I are working at opposite ends of a conveyor belt. I put on a package every four seconds and the conveyor belt delivers it to you. It is your job to remove the packages as they arrive. If I am stationary and you are stationary, packages arrive at the same rate as I place them on the conveyor belts. But what if I am moving in the same direction as the conveyor belt is moving as I place the packages on the belt. Common sense would dictate the packages of the closer together. That means that their frequency of arrival will be higher. The same analogy would work if I walked away from you while I continued to place packages on every four seconds the distance between them with the greater and frequency of arrival will be smaller.

When the speed of a wave source is equal to or exceeds the speed of the wave, a curious situation develops. In sound waves, the compression set up one on top of the other producing phenomenon called a sonic boom. (What happens in the conveyor analogy?] This phenomenon became an important consideration for airplanes flying faster than the speed of sound after World War II. See
http://www.kettering.edu/~drussell/Demos/doppler/doppler.html

http://www.phy.ntnu.edu.tw/java/Doppler/Doppler.html
http://www.explorescience.com/activities/Activity_page.cfm?ActivityID=45

It should be noted that the Doppler effect also applies to light waves. Of course, the objects in question have to be moving at very large speeds. The objects are usually stars. Stars are approaching emit light whose wavelengths are short compared to what they should be; this is known as Doppler blue shift. Stars in the moving away from us emit light whose wavelengths for longer than they should be; this is known as Doppler red shift.

http://www.silcom.com/~aludwig/musicand.htm

Resonance

Consider a large (2 liter) graduated cylinder filled to near capacity with water. Into the cylinder we place a large diameter glass tube that has open ends. As we raise and lower the tube, the length of the air column of air can be varied. Now let's place a vibrating tuning fork at the top of the tube. Every half cycle a tine pushes a compression down the tube. Because the tube is closed at the bottom, the compression reflects back to the top where it encounters the tine again. Most of the time, the reflected pulse will encounter another pulse and interfere destructively with it. But if the length of the column is just right, the returning pulse meets the tine pushing away from the tube and therefore reinforces the out going pulse. The sound produced by the tuning fork will be much louder. This magic length, L, for the column of air must be 1/4 wave length or . For a tube open at the bottom, the minimum resonant length is given by .

References - For useful references regarding this topic go to
REFERENCES.

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