While I mean no offense to you, I half expected this answer, and I think it's a bit of a cliché'd cop-out. So I think it's safe to say, based on fluid dynamics, that the damage should be massively increased, and for balance reasons, the spell should just do what it says on the tin. This is not only because of the massive speed increase that is squared, but also because water is ~1000 times more dense than air. In water, we get a whopping 1101128 kPa! That's about 10,800 atmospheres of pressure. Those calculations are a bit tougher to do, and I don't have time to run them right now, unfortunately, but suffice to say that they do not exceed the below.
This isn't the whole story, however! Remember how I said air was compressible? Well, it will have a higher density at such high speed. In sea level air, this gives a dynamic pressure of 72.060 kPa, roughly 3/4 of an atmosphere of pressure. Thankfully, this is one of the equations that doesn't get funky near or at sonic speeds: P = (0.5) * rho * v^2 Now, to better quantify just how hard that hits, we should really look at dynamic pressure, or the pressure caused by the velocity of the fluid. So despite being "quieter" underwater, the sound is actually moving much faster - 4.2 times as fast or so.
Running the numbers gives a speed of sound of ~343 m/s in air and ~1484 m/s in water. Where K is the bulk modulus of the fluid and rho is its density. Speed of sound in liquids: a = sqrt(K/rho) Where gamma is the ratio of specific heats, R is the ideal specific gas constant, and T is the temperature of the fluid. Speed of sound in gasses: a = sqrt(gamma * R * T) The equation for speed of sound in different media isn't even the same.
Mach number holds for any medium, but the speed is actually different. Sound travels at, unsurprisingly, the speed of sound, Mach 1. Water is essentially incompressible, unlike air. If we are working under the assumption that the magic creates a "normal" sound - that is, it is not an illusion of some sort, but rather physical soundwaves traversing a medium, then the spell should indeed function as written.or rather, it should probably be much more powerful. *Looks at username* Huh, guess I should chime in here. What does r/DnD think? Do we have anybody with better physics knowledge than me here to pass judgement? As such, I feel like I was in the right by saying the spell is less effective underwater. A creature made of inorganic material such as stone, crystal, or metal has disadvantage on this saving throw." I think that while a shockwave created by a grenade may be more effective underwater, the Shatter spell does not create such a shockwave: it merely creates the ear-piercing sound, without an explosion of the sorts to accompany it. A creature takes 3d8 thunder damage on a failed save, or half as much damage on a successful one. Each creature in a 10-foot-radius sphere centered on that point must make a Constitution saving throw. The description of Shatter is as follows: " A sudden loud ringing noise, painfully intense, erupts from a point of your choice within range. However, now that the ordeal is over, I am actually curious as to the physics behind it, and doubtful that my players were right. At the time I simply wanted to keep the flow of the game intact and since I wasn't sure, I erred on the side of the players and made the spell work as normal. One of them later even threw me this article about underwater grenade explosions to make his point. However, literally all my players protested to this at the same time, saying that it would in fact be more powerful because the shockwave extends further. My go-to reasoning was that as sounds are muffled underwater, it would be less effective than above the water. Hey folks! So yesterday, I was DMing a game when one of my players wanted to cast 'Shatter' under water.
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