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Elastic objects vibrate, or move back and forth, in a repeating motion when disturbed by some external force. They are able to do this because they have an internal restoring force that returns them to their original positions after being deformed by some external force. If the internal restoring force is opposite to and proportional to the deforming displacement, the vibration is called a simple harmonic motion. The extent of displacement is called the amplitude, and one complete back-and-forth motion is one cycle. The time required for one cycle is a period. The frequency is the number of cycles per second, and the unit of frequency is the hertz. A graph of the displacement as a function of time for a simple harmonic motion produces a sinusoidal graph. Periodic, or repeating, vibrations or the pulse of a single disturbance can create waves, disturbances that carry energy through a medium. A wave that disturbs particles in a back-and-forth motion in the direction of the wave travel is called a longitudinal wave. A wave that disturbs particles in a motion perpendicular to the direction of wave travel is called a transverse wave. The nature of the medium and the nature of the disturbance determine the type of wave created. Waves that move through the air are longitudinal and cause a back-and-forth motion of the molecules making up the air. A zone of molecules forced closer together produces a condensation, a pulse of increased density and pressure. A zone of reduced density and pressure is a rarefaction. A vibrating object produces condensations and rarefactions that expand outward from the source. If the frequency is between 20 Hz and 20,000 Hz, the human ear perceives the waves as sound of a certain pitch. High frequency is interpreted as high-pitched sound, and low frequency as low-pitched sound. A graph of pressure changes produced by condensations and rarefactions can be used to describe sound waves. The condensations produce crests, and the rarefactions produce troughs. The amplitude is the maximum change of pressure from the normal. The wavelength is the distance between any two successive places on a wave train, such as the distance from one crest to the next crest. The period is the time required for a wave to repeat itself. The velocity of a wave is how quickly a wavelength passes. The frequency can be calculated from the waveequation, v = λƒ. Sound waves can move through any medium but not a vacuum. The velocity of sound in a medium depends on the molecular inertia and strength of interactions. Sound, therefore, travels most rapidly through a solid, then a liquid, then a gas. In air, sound has a greater velocity in warmer air than in cooler air because the molecules of air are moving about more rapidly, therefore transmitting a pulse more rapidly. Sound waves are reflected or refracted from a boundary, which means a change in the transmitting medium. Reflected waves that are in phase with incoming waves undergo constructive interference and waves that are out of phase undergo destructive interference. Two waves that are otherwise alike but with slightly different frequencies produce an alternating increasing and decreasing of loudness called beats. The energy of a sound wave is called the wave intensity, which is measured in watts per square meter. The intensity of sound is expressed on the decibel scale, which relates it to changes in loudness as perceived by the human ear. All elastic objects have natural frequencies of vibration that are determined by the materials they are made of and their shapes.When energy is transferred at the natural frequencies, there is a dramatic increase of amplitude called resonance. The natural frequencies are also called resonant frequencies. Sounds are compared by pitch, loudness, and quality. The quality is determined by the instrument sounding the note. Each instrument has its own characteristic quality because of the resonant frequencies that it produces. The basic, or fundamental, frequency is the longest standing wave that it can make. The fundamental frequency determines the basic note being sounded, and other resonant frequencies, or standing waves called overtones or harmonics, combine with the fundamental to give the instrument its characteristic quality. A moving source of sound or a moving observer experiences an apparent shift of frequency called the Doppler effect. If the source is moving as fast or faster than the speed of sound, the sound waves pile up into a shock wave called a sonic boom. A sonic boom sounds very much like the pressure wave from an explosion. Summary of Equations
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