speed of sound

The speed of sound is the sonic velocity in the local medium and is strongly dependent on temperature. At sea level on a standard day it is approximately 1117 feet per second (761.6 mph).

The relationship of the speed of an object moving in a compressible medium to the local speed of sound indicates the level of compressibility effects it will encounter in that medium.

The speed of sound in seawater is by no means constant, depending on the water's density (and therefore on temperature, depth and salinity) but can be calculated approximately with the following equation:

c(D,S,t) = c(0,S,t) + (16.23 + 0.253t)D + (0.213-0.1t)D² + [0.016 + 0.0002(S-35)](S - 35)tD

where

c(0,S,t) = 1449.05 + 45.7t - 5.21t2 + 0.23t³ + (1.333 - 0.126t + 0.009t²)(S - 35)

and

t = T/10 where T = temperature in degrees Celsius
S = salinity in parts per thousand
D = depth in kilometers

Range of validity: temperature 0 to 35 degrees Celsius, salinity 0 to 45 parts per thousand, depth 0 to 4000 m

This equation was developed by one Dr. A.B. Coppins in 1981 and published in the Journal of the American Society of Acoustic Sciences.

The speed of sound in a fluid medium is given by

c = sqrt(dp/dρ)

where p denotes the pressure and ρ the density of the fluid. Since the bulk modulus of elasticity can be expressed as

E = ρ(dp/dρ)

we then have

c = sqrt(E/ρ)

For an isentropic process (which is assumed when we talk about acoustic waves), the bulk modulus is simply E = kp, where k is the ratio of the specific heat at constant temperature to the specific heat at constant volume. (Remember that in an isentropic process, p/ρ^k is constant; for air under standard atmospheric conditions, k = 1.40). Thus,

c = sqrt(kp/ρ)

For an ideal gas, p = ρRT, where R is the ideal gas constant and T the temperature (in K). We have finally

c = sqrt(kRT)

which means that the speed of sound in an ideal gas is proportional to the square root of the temperature. Furthermore, we see that if a fluid would really be incompressible, then E would be infinite and so would be the speed of sound.

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Primary source: Fundamentals of fluid mechanics, Munson, Young, Okiishi, Wiley Editor.

Speeds¹ (m/s) of Sound:

Gases
• Air (0° C) - 331
• Air (20° C) - 343
• Helium - 965
• Hydrogen - 1284
  
  Liquids
• Water (0° C) - 1402
• Water (20° C) - 1482
• Seawater² - 1522
  
  Solids
• Aluminum - 6420
• Steel - 5941
• Granite - 6000

1. At 0° C and 1 atm pressure, except where noted.
2. At 20° C and 3.5% salinity.

The speed of sound in air at any temperature T (in °C) can also be found using the equation v = 331 + 0.6*T. For other materials/temperatures/pressures, other writeups in this node describe formulas that can be used to calculate the speed of sound.

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Source:
Halliday, Ressnick, Walker. Fundamentals of Physics: Fourth Edition.