Underwater Sound Speed Profile Calculator
Oceanography & undersea warfare: Calculate the underwater speed of sound profile ($c(z)$) across depth, temperature, and salinity via Mackenzie and Del Grosso formulations, locating the SOFAR acoustic channel axis.
Oceanographic Profile Data
Sound Speed & SOFAR Duct Metrics
Sound Speed at Depth $c(z)$
--
m/s (@ evaluation depth)
Surface Sound Speed $c_{surf}$
--
m/s (z = 0 m)
SOFAR Channel Axis Depth
--
meters (sound speed minimum)
Minimum Sound Speed $c_{min}$
--
m/s (SOFAR duct sound speed)
Sound Speed Gradient $g$
--
$s^{-1}$ ($dc/dz$ local gradient)
Acoustic Ray Radius $R_{ray}$
--
km (refractive bend radius)
Sound Speed Profile (Depth vs Velocity)
Temperature drops rapidly through the thermocline, lowering sound speed. Below the SOFAR axis, hydrostatic pressure dominates, bending rays continuously back toward the channel axis.
The Mackenzie (1981) Nine-Term Equation
The empirical Mackenzie equation provides the speed of sound $c$ in seawater as a function of temperature $T$ (°C), salinity $S$ (parts per thousand), and depth $z$ (meters):
$$c = 1448.96 + 4.591 T - 5.304 \times 10^{-2} T^2 + 2.374 \times 10^{-4} T^3 + 1.340(S - 35) + 1.630 \times 10^{-2} z + 1.675 \times 10^{-7} z^2 - 1.025 \times 10^{-2} T(S - 35) - 7.139 \times 10^{-13} T z^3$$
Rule of thumb: Sound speed increases by $\approx 4.0 \text{ m/s}$ per $1^\circ\text{C}$ temperature rise, $\approx 1.3 \text{ m/s}$ per 1 ppt salinity increase, and $\approx 1.7 \text{ m/s}$ per 100 meters of water depth.
Recommended Tools & Equipment
Tested hardware and components for high reliability
100% Free Tool
Zero Sign-Up