Speed of Sound (or Velocity of Sound)


Speed of Sound (or Velocity of Sound) :

The speed with which a sound wave advances through a medium. The speed of sound varies widely from one medium to another and depends upon the physical state of any given medium, but this is not strongly dependent upon the frequency of the sound wave. Only in the case of ultrasonic waves does one have to take account of dispersion effects, and even then this is important only in gases. For all media, the speed of sound V is given by: V = VATp where K is the modulus of elasticity of the medium (for fluids, the bulk modulus) and p is its density. Newton, mistakenly regarding the passage of a sound wave as an isothermal process, concluded that K for fluids must be simply the pressure itself. Laplace in 1816, recognizing that the rapidity with which sonic rarefactions and compressions follow each other implied adiabaticity, showed that the effective bulk modulus A" is the product of pressure times the ratio y of the specific heat at constant pressure to that at constant volume of the medium in question. In the case of a perfect-gas medium, substitution from the equation of state gives, in all, V = VyfiT where p is the pressure, R is the gas constant for one gram of the gas in question, and T is its absolute temperature. In air at 0oC, V is 331.4 m/sec or 1087.8 ft/sec; in water at 13oC, v is 1441 m/sec; in steel at 0oC, V is about 5000 m/sec. See Laplacian speed of sound, Newtonian speed of sound. N.B. Refer to source to verify equation(s)

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