Speed of sound: Difference between revisions

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	The '''speed of sound''' varies depending on the medium through which the ] waves pass. It is usually quoted in describing properties of substances (e.g. see the article on ]).		The '''speed of sound''' c varies depending on the medium through which the ] waves pass. It is usually quoted in describing properties of substances (e.g. see the article on ]).

	More commonly the term refers to the speed of sound in ]. In this case the physical properties of the air, its ~~] and~~ ] ~~for~~ ~~instance,~~ ~~affect~~ the speed. An approximate speed (in metres/second) can be calculated from:		More commonly the term refers to the speed of sound in ]. In this case the physical properties of the air, its ], affect very little the speed. An approximate speed (in metres/second) can be calculated from:

	:<math>v = 331 + (0.6T)</math>		:<math>c = 331 + (0.6T)</math>

	where ''T'' is the temperature in degrees ]		where ''T'' is the temperature in degrees ]
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	A more accurate expression is		A more accurate expression is

	:<math>v = \sqrt{\gamma RT}</math>		:<math>c = \sqrt{\gamma RT}</math>

	where ''R'' is the ] (287 J/kgK for air), γ is the ] (1.4 for air), and ''T'' is the absolute temperature in ]. In the standard atmosphere, ''T''<sub>0</sub> is 288.15 K, giving a value of 346 m/s.		where ''R'' is the ] (287 J/kgK for air), γ is the ] (1.4 for air), and ''T'' is the absolute temperature in ]. In the standard atmosphere, ''T''<sub>0</sub> is 288.15 K, giving a value of 346 m/s.
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	In fluids, using the theory of ], the speed of sound can be calculated using		In fluids, using the theory of ], the speed of sound can be calculated using

	:<math>v = \sqrt{{\gamma p}\over\rho}</math>		:<math>c = \sqrt{{\gamma p}\over\rho}</math>

	This is correct for adiabatic flow; Newton famously used isothermal calculations and omitted the γ from the numerator.		This is correct for adiabatic flow; Newton famously used isothermal calculations and omitted the γ from the numerator.
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	In solids the speed of sound is given by:		In solids the speed of sound is given by:

	:<math>v = \sqrt{\frac{E}{\rho}}</math>		:<math>c = \sqrt{\frac{E}{\rho}}</math>

	where ''E'' is ] and ρ is ]. Thus in ] the speed of sound is approximately 5100 m/s.		where ''E'' is ] and ρ is ]. Thus in ] the speed of sound is approximately 5100 m/s.

Revision as of 22:58, 3 March 2004

The speed of sound c varies depending on the medium through which the sound waves pass. It is usually quoted in describing properties of substances (e.g. see the article on sodium).

More commonly the term refers to the speed of sound in air. In this case the physical properties of the air, its humidity, affect very little the speed. An approximate speed (in metres/second) can be calculated from:

c=331+(0.6T)

where T is the temperature in degrees Celsius

A more accurate expression is

c={\sqrt {\gamma RT}}

where R is the gas constant (287 J/kgK for air), γ is the adiabatic index (1.4 for air), and T is the absolute temperature in kelvin. In the standard atmosphere, T₀ is 288.15 K, giving a value of 346 m/s.

In fluids, using the theory of compressible flow, the speed of sound can be calculated using

c={\sqrt {{\gamma p} \over \rho }}

This is correct for adiabatic flow; Newton famously used isothermal calculations and omitted the γ from the numerator.

The speed of sound is typically measured given a "standard atmosphere". Under these conditions the speed of sound is approximately 346 m/s at 25°C, or 750 miles/hour.

In solids the speed of sound is given by:

c={\sqrt {\frac {E}{\rho }}}

where E is Young's modulus and ρ is density. Thus in steel the speed of sound is approximately 5100 m/s.

The speed of sound in water is of interest to those mapping the ocean floor. In saltwater, sound travels at about 1500 m/s and in freshwater 1435 m/s. These speeds vary due to pressure, depth, temperature, salinity and other factors.