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I have been watching programmes commemorating the Apollo 11 mission. One obvious feature of the launch is the sound. It was mentioned that water was sprayed into the pit below the rocket not (primarily) for cooling as you may expect but to prevent the sound energy bouncing back from the concrete and damaging the engines.

I expect that there are very many inefficiencies in a real rocket and far more fuel is required that a naive application of the Tsiolkovsky rocket equation (Wikipedia) would suggest. One of these inefficiencies, probably not the largest, is the energy lost as sound.

Has this been estimated? Is it significant? Clearly, a Saturn V launch generates a lot of sound energy but it could still be a small fraction of the energy in its fuel.

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Yes, these topics are widely studied in the field of aeroacoustics, thermoacoustics or generally compressible fluid dynamics. The combustion is literally a hot topic. This series might be interesting for you and there is also a book from T. C. Lieuwen approaching this topic (and certainly it is not the only one).

Usually the energy loss due to sound emission presents relatively small part of the overall energy (for cold subsonic flows it is proportional at best to the third power of Mach number). The issues might arise when some sort of feedback-loop is triggered, resulting (for example) in strong standing waves in the combustion chambre or some sort of enclosure.

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