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Speed of sound

The velocity of sound in air is 770 mi/hr. This speed, however, is influenced by temperature and air pressure.

The speed of sound is the distance traveled per unit time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 meters per second (1,235 km/h; 1,125 ft/s; 767 mph; 667 kn), or a kilometer in 2.9 s or a mile in 4.7 s. It depends strongly on temperature but also varies by several meters per second, depending on which gases exist in the medium through which a soundwave is propagating.

The speed of sound in an ideal gas depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slightly from ideal behavior.

In common everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance: sound travels most slowly in gases; it travels faster in liquids; and faster still in solids. For example, (as noted above), sound travels at 343 m/s in air; it travels at 1,480 m/s in water (4.3 times as fast as in air), and at 5,120 m/s in iron (about 15 times as fast as in air). In an exceptionally stiff material such as diamond, sound travels at 12,000 meters per second (39,000 ft/s)—about 35 times as fast as in air—which is around the maximum speed that sound will travel under normal conditions.

Sound waves in solids are composed of compression waves (just as in gases and liquids), and a different type of sound wave called a shear wave, which occurs only in solids. Shear waves in solids usually travel at different speeds, as exhibited in seismology. The speed of compression waves in solids is determined by the medium's compressibility, shear modulus, and density. The speed of shear waves is determined only by the solid material's shear modulus and density.

In fluid dynamics, the speed of sound in a fluid medium (gas or liquid) is used as a relative measure for the speed of an object moving through the medium. The ratio of the speed of an object to the speed of sound in the fluid is called the object's Mach number. Objects moving at speeds greater than Mach1 are said to be traveling at supersonic speeds.

The transmission of sound can be illustrated by using a model consisting of an array of spherical objects interconnected by springs.

In real material terms, the spheres represent the material's molecules and the springs represent the bonds between them. Sound passes through the system by compressing and expanding the springs, transmitting the acoustic energy to neighboring spheres. This helps transmit the energy in-turn to the neighboring sphere's springs (bonds), and so on.

The speed of sound through the model depends on the stiffness/rigidity of the springs, and the mass of the spheres. As long as the spacing of the spheres remains constant, stiffer springs/bonds transmit energy quicker, while larger spheres transmit the energy slower.

In a real material, the stiffness of the springs is known as the "elastic modulus", and the mass corresponds to the material density. Given that all other things being equal (ceteris paribus), sound will travel slower in spongy materials, and faster in stiffer ones. Effects like dispersion and reflection can also be understood using this model.

For instance, sound will travel 1.59 times faster in nickel than in bronze, due to the greater stiffness of nickel at about the same density. Similarly, sound travels about 1.41 times faster in light hydrogen (protium) gas than in heavy hydrogen (deuterium) gas, since deuterium has similar properties but twice the density. At the same time, "compression-type" sound will travel faster in solids than in liquids, and faster in liquids than in gases, because the solids are more difficult to compress than liquids, while liquids in turn are more difficult to compress than gases.

Some textbooks mistakenly state that the speed of sound increases with density. This notion is illustrated by presenting data for three materials, such as air, water and steel, they each have vastly different compressibility,which more than makes up for the density differences. An illustrative example of the two effects is that sound travels only 4.3 times faster in water than air, despite enormous differences in compressibility of the two media. The reason is that the larger density of water, which works to slow sound in water relative to air, nearly makes up for the compressibility differences in the two media.

A practical example can be observed in Edinburgh when the "One o' Clock Gun" is fired at the eastern end of Edinburgh Castle. Standing at the base of the western end of the Castle Rock, the sound of the Gun can be heard through the rock, slightly before it arrives by the air route, partly delayed by the slightly longer route. It is particularly effective if a multi-gun salute such as for "The Queen's Birthday" is being fired.

Key Terms

air
density
gases
liquids
solids
sound
speed sound
spheres
springs
times

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Speed of sound
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Last modified on July 15 2019
Content adapted from Wikipedia
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