Numworks: Estimating the Speed of Sound in Water
Generally, the speed of sound in water is faster than the speed of sound in air. Is there an easy way to estimate the speed of sound in water using curve fitting? I will use the Numworks’ Regression App. The online simulator of Numworks: https://www.numworks.com/simulator/ .
* For readability, I consolidated some screen shots.
The data, from The Engineering Toolbox (see Source below) is shown in below:
SI Units
Temperature in °C | Speed of sound in m/s (meters/second) |
0 | 1403 |
5 | 1427 |
10 | 1447 |
20 | 1481 |
30 | 1507 |
40 | 1526 |
50 | 1541 |
60 | 1552 |
70 | 1555 |
80 | 1555 |
90 | 1550 |
100 | 1543 |
https://www.engineeringtoolbox.com/sound-speed-water-d_598.html
Of the curve fits available, I found the best fits were to be with polynomial regression.
Quadratic Regression: y = a2 * x^2 + a1 * x + a0
y = -0.02736013 * x^2 + 4.059449 * x + 1407.3398
where y is the speed of sound in water (m/s) and x is the temperature (°C). The r^2 parameter is 0.9980768, which is pretty good given the raw data is only rounded the nearest integer. The Numworks also offers residual plot, which is the difference between predicted and given data. From the residual plot, the biggest difference was at x = 0.
Quartic Regression: y = a4 * x^4 + a3 * x^3 + a2 * x^2 + a1 * x + a0
If we are looking for better accuracy, we could use the quartic regression, where r^2 parameter is 0.99981. From the residual plot, the biggest difference was located at x = 60.
y = -7.955665 * 10^-7 * x^4 + 2.523644 * 10^-4 * x^3 – 0.05122094 * x^2 + 4.782147 * x + 1403.692
For a quick calculation, the quadratic equation could be sufficient enough.
Source
The Engineering ToolBox (2004). Water - Speed of Sound vs. Temperature. [online] Available at: https://www.engineeringtoolbox.com/sound-speed-water-d_598.html. Accessed May, 2025.
Eddie
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The author does not use AI engines and never will.
