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Bilaniuk and Wong

Interactive Version

a) 112 point equation

c =	1.40238742 x 103 + 5.03821344 T - 5.80539349 x 10-2 T2 + 3.32000870 x 10-4 T3 - 1.44537900 x 10-6 T4 + 2.99402365 x 10-9 T5

b) 36 point equation

c =	1.40238677 x 103 + 5.03798765 T - 5.80980033 x 10-2 T2 + 3.34296650 x 10-4 T3 - 1.47936902 x 10-6 T4 + 3.14893508 x 10-9 T5

c) 148 point equation

c =	1.40238744 x 103 + 5.03836171 T - 5.81172916 x 10-2 T2 + 3.34638117 x 10-4 T3 - 1.48259672 x 10-6 T4 + 3.16585020 x 10-9 T5
	T = temperature in degrees Celsius

Range of validity: 0-100 °C at atmospheric pressure

Bilaniuk and Wong (1993,1996) converted Del Grosso and Mader's 1972 data to the 1990 International Temperature Scale and then produced three sets of coefficients depending on the number of temperature points which were converted and taken into account in their data fitting routines.

Marczak

Interactive Version

c =	1.402385 x 103 + 5.038813 T - 5.799136 x 10-2 T2 + 3.287156 x 10-4 T3 - 1.398845 x 10-6 T4 + 2.787860 x 10-9 T5
	T = temperature in degrees Celsius

Range of validity: 0-95°C at atmospheric pressure.

Marczak (1997) combined three sets of experimental measurements, Del Grosso and Mader (1972), Kroebel and Mahrt (1976) and Fujii and Masui (1993) and produced a fifth order polynomial based on the 1990 International Temperature Scale.

Lubbers and Graaff's simplified equations

Interactive Version

a)

A simple equation for use in the temperature interval 15-35°C

c =	1404.3 + 4.7T - 0.04 T2

Range of validity: 15-35°C at atmospheric pressure. Claimed accuracy - maximum error 0.18 ms^-1

b)

c =	1405.03 + 4.624 T - 3.83 x 10 -2 T2

Range of validity: 10-40°C at atmospheric pressure

Lubbers and Graaff (1998) produced these simple equations with a restricted temperature range for medical ultrasound applications, including tissue mimicking materials and test objects. Within the quoted temperature ranges they claim that the maximum error is approximately 0.18 ms^-1 in comparisons with experimental data and more detailed equations such as Bilaniuk and Wong (1993,1996).

Belogol'skii, Sekoyan et al: speed of sound as a function of temperature and pressure

Interactive Version

c(T,P) =	c(T,0) + M1(T)(P - 0.101325) + M2(T) (P- 0.101325)2 + M3(T)(P - 0.101325)3
c(T,0) =	a00 + a10T + a20T2 + a30T3 + a40T4 + a50T5
M1(T) =	a01 + a11T + a21T2 + a31T3
M2(T) =	a02 + a12T + a22T2 + a32T3
M3(T) =	a03 + a13T + a23T2 + a33T3
	T = temperature in degrees Celsius P = pressure in megapascals

Range of validity: 0-40°C, 0.1 - 60 MPa
This version uses the 1990 International Temperature Scale

Belogol'skii, Sekoyan et al (1999) made their own measurements of sound speed as a function of pressure and temperature and also used the equation of Bilaniuk and Wong (1996) for sound speed at atmospheric pressure.

Table of Coefficients Coefficient Numerical value a00 1402.38744 a10 5.03836171 a20 -5.81172916 x 10-2 a30 3.34638117 x 10-4 a40 -1.48259672 x 10-6 a50 3.16585020 x 10-9 a01 1.49043589 a11 1.077850609 x 10-2 a21 -2.232794656 x 10-4 a31 2.718246452 x 10-6 a02 4.31532833 x 10-3 a12 -2.938590293 x 10-4 a22 6.822485943 x 10-6 a32 -6.674551162 x 10-8 a03 -1.852993525 x 10-5 a13 1.481844713 x 10-6 a23 -3.940994021 x 10-8 a33 3.939902307 x 10-10

Any comments or suggestions about further speed of sound equations?

Please contact Justin Ablitt .