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Lesson 1: The Nature of a Sound Wave

Mechanical Wave

Longitudinal Wave

Pressure Wave

 

 

Lesson 2: Sound Properties and Their Perception

Pitch and Frequency

Intensity/Decibel Scale

The Speed of Sound

The Human Ear

 

 

Lesson 3: Behavior of Sound Waves

Interference and Beats

The Doppler Effect and Shock Waves

Boundary Behavior

Reflection, Refraction, and Diffraction

 

 

Lesson 4: Resonance and Standing Waves

Natural Frequency

Forced Vibration

Standing Wave Patterns

Fundamental Frequency and Harmonics

 

 

Lesson 5: Musical Instruments

Resonance

Guitar Strings

Open-End Air Columns

Closed-End Air Columns

Lesson 1: The Nature of a Sound Wave

Sound is a Pressure Wave

Sound is a mechanical wave which results from the back and forth vibration of the particles of the medium through which the sound wave is moving. If a sound wave is moving from left to right through air, then particles of air will be displaced both rightward and leftward as the energy of the sound wave passes through it. The motion of the particles are parallel (and anti-parallel) to the direction of the energy transport. This is what characterizes sound waves in air as longitudinal waves.

A vibrating tuning fork is capable of creating such a longitudinal wave. As the tines of the fork vibrate back and forth, they push on neighboring air particles. The forward motion of a tine pushes air molecules horizontally to the right and the backward retraction of the tine creates a low pressure area allowing the air particles to move back to the left.

Because of the longitudinal motion of the air particles, there are regions in the air where the air particles are compressed together and other regions where the air particles are spread apart. These regions are known as compressions and rarefactions respectively. The compressions are regions of high air pressure while the rarefactions are regions of low air pressure. The diagram below depicts a sound wave created by a tuning fork and propagated through the air in an open tube. The compressions and rarefactions are labeled.

The wavelength of a wave is merely the distance which a disturbance travels along the medium in one complete wave cycle. Since a wave repeats its pattern once every wave cycle, the wavelength is sometimes referred to as the length of the repeating pattern - the length of one complete wave. For a transverse wave, this length is commonly measured from one wave crest to the next adjacent wave crest or from one wave trough to the next adjacent wave trough. Since a longitudinal wave does not contain crests and troughs, its wavelength must be measured differently. A longitudinal wave consists of a repeating pattern of compressions and rarefactions. Thus, the wavelength is commonly measured as the distance from one compression to the next adjacent compression or the distance from one rarefaction to the next adjacent rarefaction.

Since a sound wave consists of a repeating pattern of high pressure and low pressure regions moving through a medium, it is sometimes referred to as a pressure wave. If a detector, whether it be the human ear or a man-made instrument, is used to detect a sound wave, it would detect fluctuations in pressure as the sound wave impinges upon the detecting device. At one instant in time, the detector would detect a high pressure; this would correspond to the arrival of a compression at the detector site. At the next instant in time, the detector might detect normal pressure. And then finally a low pressure would be detected, corresponding to the arrival of a rarefaction at the detector site. The fluctuations in pressure as detected by the detector occur at periodic and regular time intervals. In fact, a plot of pressure versus time would appear as a sine curve. The peak points of the sine curve correspond to compressions; the low points correspond to rarefactions; and the "zero points" correspond to the pressure which the air would have if there were no disturbance moving through it. The diagram below depicts the correspondence between the longitudinal nature of a sound wave in air and the pressure-time fluctuations which it creates at a fixed detector location.

 

The above diagram can be somewhat misleading if you are not careful. The representation of sound by a sine wave is merely an attempt to illustrate the sinusoidal nature of the pressure-time fluctuations. Do not conclude that sound is a transverse wave which has crests and troughs. Sound waves traveling through air are indeed longitudinal waves with compressions and rarefactions. As sound passes through air (or any fluid medium), the particles of air do not vibrate in a transverse manner. Do not be misled - sound waves traveling through air are longitudinal waves.

 

 

 

Check Your Understanding

1. A sound wave is a pressure wave; regions of high (compressions) and low pressure (rarefactions) are established as the result of the vibrations of the sound source. These compressions and rarefactions result because sound

a. is more dense than air and thus has more inertia, causing the bunching up of sound.

b. waves have a speed which is dependent only upon the properties of the medium.

c. is like all waves; it is able to bend into the regions of space behind obstacles.

d. is able to reflect off fixed ends and interfere with incident waves

e. vibrates longitudinally; the longitudinal movement of air produces pressure fluctuations.

 

 

 

 

 

Lesson 1: The Nature of a Sound Wave

 

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