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Author: Elliot Richmond
Editor: Mary Rose Bonk
Date: 2016
From: Mathematics(Vol. 4. 2nd ed.)
Publisher: Gale, a Cengage Company
Document Type: Topic overview
Length: 1,025 words
Content Level: (Level 3)
Lexile Measure: 1010L

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Page 39


Sound is produced by the vibration of some sort of material. In a piano, a hammer strikes a steel string, causing the string to vibrate. A guitar string is plucked and vibrates. A violin string vibrates when it is bowed. In a saxophone, the reed vibrates. In an organ pipe, the column of air vibrates. When a person speaks or sings, two strips of muscular tissue in the throat vibrate. All of the vibrating objects produce sound waves.

Characteristics of Waves

All waves, including sound waves, share certain characteristics: They travel through material at a certain speed, they have frequency, and they have wavelength. The frequency of a wave is the number of waves that pass a point in one second. The wavelength of a wave is the distance between any two corresponding points on the wave. For all waves, there is a simple mathematical relationship between these three quantities called the wave equation. If the frequency is denoted by the symbol f the wavelength is denoted by the symbol λ, and the symbol v denotes the velocity, then the wave equation is v = f λ. In a given medium, a sound wave with a shorter wavelength will have a higher frequency.

Waves also have amplitude. Amplitude is the “height” of the wave, or how “big” the wave is. The amplitude of a sound wave determines how loud its sound is.

Longitudinal Waves Sound waves are longitudinal waves. That means that the part of the medium vibrating moves back and forth instead of up and down or from side to side. Regions where the particles of the medium are pushed together are called compressions. Places where the particles are pulled apart are called rarefactions. A sound wave consists of a series of compressions and rarefactions moving through the medium.

As with all types of waves, the medium is left in the same place after the wave passes. A person watching and listening to a television across the room receives sound waves that are moving through the air, but the air is not moving across the room.

Speed of Sound Waves Sound travels through solids, liquids, and gases at different speeds. The speed depends on the springiness of the medium. Steel, for example, is much springier than air, so sound travels through steel about 15 times faster than it travels through air.

At 0°C, sound travels through dry air at about 331 meters per second. The speed of sound increases with temperature and humidity. The speed of sound in air is related to many important thermodynamic Page 40  |  Top of Articleproperties of air. Since the speed of sound in air measures how fast a wave of pressure will move through air, anything that depends on air pressure will be expected to behave differently near the speed of sound. This characteristic caused designers of high-speed aircraft many problems. Before the design problems were overcome, several test pilots lost their lives trying to “break the sound barrier.”

The speed of sound increases by 0.6 meter per second (m/s) for each Celsius degree rise in temperature (T). This information can be used to construct a formula for the speed (v) of sound at any temperature:

v = (331 + 0.60T)m/s

At average room temperature of 20°C, the speed of sound is close to 343 meters per second.

Frequency and Pitch Sounds can have different frequencies. The frequency of the sound is the number of times the object vibrates per second. Frequency is measured in vibrations per second, or hertz (Hz). One Hz is one vibration per second. Humans perceive different frequencies of sound as different pitches; as a consequence, the higher the frequency, the higher the pitch. The normal human ear can detect sounds with frequencies between 20 Hz and 20,000 Hz. As humans age, the upper limit usually drops. Dogs can hear much higher frequencies, up to 50,000 Hz. Bats can detect frequencies up to 100,000 Hz.

The sound at a heavy metal concert is about a billion times the intensity of a whisper but is perceived as only about 800 times as loud because humans perceive sound on a logarithmic scale. The sound at a heavy metal concert is about a billion times the intensity of a whisper but is perceived as only about 800 times as loud because humans perceive sound on a logarithmic scale. © Mauricio Santana/Corbis Entertainment/Corbis © Mauricio Santana/Corbis Entertainment/Corbis

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Intensity and Perception of Sound

Sound waves, like all waves, transport energy from one place to another. The rate at which energy is delivered is called power and is measured in watts. Sound intensity is measured in watts per square meter (W/m2).

The human ear can detect sound intensity levels as low as 10-12 W/m2 and as high as 1.0 W/m2. This is an incredible range. Because of the wide range of sound intensity that humans can hear, humans perceive loudness instead of intensity. A sound with 10 times the intensity in watts per square meter is perceived as being only about twice as loud.

Since humans do not perceive sound intensity directly, a logarithmic scale * for loudness was developed. The unit of loudness is the decibel (dB), named after Alexander Graham Bell. The threshold of hearing— 0 dB—represents a sound intensity of 10-12 W/m2. Each tenfold increase in intensity corresponds to 10 dB on the loudness scale. Thus, 10 dB is 10 times the sound intensity of 0 dB. A sound of 20 dB is 10 times the intensity of a 10 dB sound and 100 times the intensity of a 0 dB sound. The list below shows the loudness of some common sounds.


Even short exposure to sounds above 120 dB will cause permanent damage to hearing. Longer exposure to sounds just below 120 dB will also cause permanent damage.

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Elliot Richmond

*logarithmic scale a scale in which the distances that numbers are positioned, from a reference point, are proportional to their logarithms


Cox, Trevor. The Sound Book: The Science of the Sonic Wonders of the World. New York: W. W. Norton, 2015.

Nuñez, Michael. “Speakers That Cut through Noise.” Popular Science (August 2015): 21.

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Gale Document Number: GALE|CX3630100278