Sound speed in pure water. Bilaniuk & Wong 36 point equation

Mathematical definition

$$\boxed{C\left( T \right) = {k_0} + {k_1}T + {k_2}{T^2} + {k_3}{T^3} + {k_4}{T^4} + {k_5}{T^5}}$$

Notation	Description	Units	Limits
$C$	sound speed	$\text{m/s}$
$T$	temperature	$^{\circ}\text{C}$	$0 < T < 100$

Coefficient	Value
$k_{0}$	$+1.40238677 \times 10^{3}$
$k_{1}$	$+5.03798765$
$k_{2}$	$-5.80980033 \times 10^{-2}$
$k_{3}$	$+3.34296650 \times 10^{-4}$
$k_{4}$	$-1.47936902 \times 10^{-6}$
$k_{5}$	$+3.14893508 \times 10^{-9}$

Octave/Matlab implementation

function C = sound_speed_water_bilaniuk_36(T)
% Inputs
%    T: temperature \ degree Celsius \ 0 < T < 100
% Outputs
%    C: speed of sound in pure water \ m/s

    k0 = +1.40238677e+3;
    k1 = +5.03798765e+0;
    k2 = -5.80980033e-2;
    k3 = +3.34296650e-4;
    k4 = -1.47936902e-6;
    k5 = +3.14893508e-9;

    C = k0*(T.^0) + k1*(T.^1) + k2*(T.^2) ...
        + k3*(T.^3) + k4*(T.^4) + k5*(T.^5);
end

Computational examples

References

1. Bilaniuk, Nykolai; Wong, George SK, "Speed of sound in pure water as a function of temperature", 1993
2. Bilaniuk, Nykolai; Wong, George SK, "Erratum: Speed of sound in pure water as a function of temperature [J. Acoust. Soc. Am. 93, 1609–1612 (1993)]", 1996