# What happens when buoyant force causes movement to exceed sound speed?

I was wondering if it is possible for an object of a certain material to be put in a buoyant medium in such a way that the buoyant force (caused by the pressure difference “above” and “below” said object and by the interactions with molecules of the medium under that regime) creates an acceleration that causes a motion that exceeds the sound speed of the material of the object.

With “sound speed” I mean the speed at which molecular interactions inside the object propagate - averagely speaking of course. Note that I’m concerned with the sound speed of the object, not of the medium!

Since this movement “ripples” through the object as it snakes upwards to get a new position in the medium, there is a limit as to how fast this type of slinky movement can happen, right?

I am wondering what happens to the movement of the object as it approaches or exceeds this limit and if some aspects of buoyancy (perhaps dynamic friction) would make this construction impossible.

Also wondering if this happens commonly in nature.

Thanks for any insights!

High buoyancy and low speed of sound have conflicting requirements. A low molecular weight increases buoyancy but it also increases the speed of sound at a given temperature. Similarly, for a gas a at least, high temperature increases buoyancy but it also increases the speed of sound. How about a liquid or solid at very low temperature? The mere act of condensation brings the molecules so much closer together that the speed of sound increases. To lower it back down again you must increase the molecular weight, which reduces buoyancy. The only variable left to play with is pressure: for a gas, low pressures increase buoyancy up to a point but has no effect on temperature. On the other hand, if the molecular weights of the object and medium differ considerably, then pressure has ittle effect on buoyancy either. All, in all, even if it were possible to find a combination of materials and states which fulfilled the basic criteria, it would only be by a modest amount. But see below.

The killer then is drag, caused primarily by frontal area, skin area and poor streamlining. A long, thin object has lowest frontal area, a sphere the lowest skin area but worse streamlining. So you are caught with a teardrop-shaped compromise. Drag rises with the fourth power of speed, so you do not have to go very fast before it equals the buoyancy. This speed is known as the terminal velocity. Your only hope for near-sonic speeds for any medium would be a frictionless fluid, i.e. superfluid helium below 2.1768 deg K (says Wikipedia), and probably confined in a capillary tube, making your experiment microscopic (I'm not sure at what scale the transition to conventional drag occurs, but it is small).

You now have to find a material which is less dense at this temperature than liquid helium. There are no gases down there and no other liquids, even hydrogen is solid. Aha! Solid hydrogen is less dense (0.0763 g/ml) than superfluid helium (ca. 0.13 g/ml).

So there you have it. A microscopic grain of solid hydrogen in an arbitrarily tall capillary tube filled with superfluid helium. I look forward to your posting on ArXiv ;)

• I believe you are talking about the speed of sound of the medium and not that of the object? Commented May 24, 2020 at 12:41
• Oh, silly me. I have now totally rewritten my reply and stood my conclusion on its head. Commented May 24, 2020 at 15:40
• Hah, thanks so much for sharing your knowledge by the way :) Commented May 24, 2020 at 16:28

I was wondering if it is possible for an object of a certain material to be put in a buoyant medium in such a way that the buoyant force (caused by the pressure difference “above” and “below” said object and by the interactions with molecules of the medium under that regime) creates an acceleration that causes a motion that exceeds the sound speed of the material of the object.

I cannot think of scenario where this is possible (though that's not saying much) outside of a plasma. However, assume it were possible to accelerate, say, a balloon fast enough to exceed the speed of sound of the gas within the balloon. What then? Is that along the lines of your question?

If so, then let's assume the balloon were made of impermeable material (don't want it rupturing). In this scenario, the result would be one side of the balloon acting like a piston to generate a shock wave. The shock would technically be between those reflected off the balloon wall and the still incident particles.

Since this movement “ripples” through the object as it snakes upwards to get a new position in the medium, there is a limit as to how fast this type of slinky movement can happen, right?

This is a different question. The "ripples" to which you refer would be in the balloon material, not the medium contained within. I use the balloon example because the sound speed in nearly all solids is so high as to be physically restrictive for the thought experiment. These "ripples" would propagate at the speed of sound in the balloon material (e.g., some type of latex polymer or rubber), which is at least an order of magnitude higher than the speed of sound in the gas contained within (unless the whole balloon is crushed such that the pressure within is extremely large).

I am wondering what happens to the movement of the object as it approaches or exceeds this limit and if some aspects of buoyancy (perhaps dynamic friction) would make this construction impossible.

I think there are several other issues rendering this idea impossible (or just not feasibly testable). For instance, suppose we put our indestructable balloon at the bottom of the Mariana's trench and let it go. The buoyant force would be huge and the balloon would accelerate quickly, but fluid drag would prevent the speed from getting too large. That is, the terminal speed is limited by the drag on the accelerating and expanding balloon (cross section increases as it rises in, say, water).

• The question had a lot of degrees of freedom for misinterpretation but I was indeed referring to the material of the balloon itself and the way buoyancy causes ripples through it. The “air” in your balloon just serves to maximise its volume so it can interact with more molecules without weighing it down too much for the buoyant force. Commented May 24, 2020 at 12:39

A signal can indeed propagate through a body faster than the speed of sound; that's what you call a shock wave. Therefore, if the buoyancy force causes the particles at the bottom of an object to acquire a speed larger than that of sound, a shock wave will be generated and will propagate upwards through the object. The propagation speed of the shock is proportional to the mean velocity of the particles, and is larger than the speed of sound.

• Question is then if buoyancy can cause shockwaves in the submerged object. It would seem like the speed of sound of the medium is always lower than that of the object in most examples, so the shockwaves would be present in the medium as well. But is this required? And what happens to the complexity/equilibrium if these shock waves are created in the object and/or the medium? Commented May 24, 2020 at 12:44