### A difference of a few knots

When planning ship speed, shipping companies face a daunting challenge, as there are many parameters to take into account. It's an optimisation between fuel consumption for transport, crew maintenance and port visits (ultimately port visits make the money).

Because power to overcome friction rises with the cube of the speed, $https://en.wikipedia.org/wiki/Drag_(physics)$ (wikipedia), reducing the speed of the ship can really cut the power needs and therefore fuel consumption.

Another thing that decreases drastically with speed reductions is the associated noise level. The following graph is from Arveson & Venditis 2000 (more detail here) and shows a noise spectrum for a given bulk cargo ship at different propeller speeds.
I modelled the two cases, one at propeller speed 140 rpm and on at 105 rpm, corresponding to a 25 % decrease in prop speed. I admit I do not know what the corresponding vessel speeds are, but I assume it translates to less then a 25 % reduction in speed, as less propeller slip is expected at lover rpms.

The noise reduction is roughly 10 dB, corresponding to a reduction in sound pressure of 68 % or a reduction in sound intensity of 90 % (noise from ships are in large part due to cavitation, a quite interesting phenomenon). I wanted to see what the reduction in noise looked like in the real (modelled) world.

At 140 rpm
 The cargo ship en route between  Liverpool and Dublin with a prop speed of 140 rpm. Noise "leaks" out of the Irish sea into the Atlantic. The depth can be seen in the window on the right.
At 105 rpm
 The cargo ship en route between  Liverpool and Dublin with a prop speed of 105 rpm. Noise is confined to the middle parts of the Irish sea. The depth can be seen in the window on the right.
The colours in these plots correspond to levels (dB) above NOAA high frequency mammal thresholds (think porpoises and dolphins).

I opted to do these plots as GIF files (how-to here) because it gives you a great overview of what the noise behaves like at different depths as well as the area affected.