[Antonio Freixas]

OK, good. Your original “air wouldn’t get there in time” had me worried. Pressure waves (regions where pressures differ) travel at the speed of sound (sound is a pressure wave). This is 343 m/s, but I prefer to think of it as 2.92 ms/m. The distance from the bladder to a reed is what, 20 mm? So a pressure wave could move across that distance in 58.4 microseconds. A pressure wave could cross the entire air chamber in about 1.168 ms.

I’m also not sure why you mentioned viscosity. Everything I am going to describe will work with a perfect gas, which is considered an inviscid fluid.

The physics at the reed is a bit more complicated than what you described, because when the reed enters the hole in the reed plate, the flow is almost entirely cut off. You described the physics as if the tongue were removed, but that’s fine for our purposes.

Even then, the pressure gradients are much more complex. The continuity equation tells us the speed of the flow changes depending on the cross-section of the system. Bernoulli’s equation tells us that as speed increases, pressure drops and vice versa. So the (static) pressure would be lowest through the reed plate and highest in the air chamber.

Let’s analyze some specific situations. We’ll start with a pressurized chamber. You place your tongue over the mouthpiece to block any loss of pressure and to keep you from adding to the flow. You open a key. With a rigid air chamber, you get your quick “puff”–just enough air to equalize the density of the inside air to that of the outside. And the air speed through the reed probably drops the closer you get to equal density. We’re in agreement here.

If you have a bladder, it has the ability to maintain the pressure longer. The elastic tension from the bladder powers the air. In this case, the air chamber is shrinking, so you can maintain the higher air density–and pressure–longer. Again, I think we’ve reached the same conclusion even if we might quibble on a few of the fine points.

Now, for the big question: why is this desirable? When you blow harder, I would think the bladder would keep the pressure from rising as fast as without (since some air goes into an expanding bladder) and when you blow less hard, it would keep the pressure from dropping (since the bladder would shrink and contribute some air).

This should play hell with vibratos. Vibratos might be off-phase a bit and might never get very loud. Of course, that’s from my back-of-envelope estimate. I’d rather hear whether a bass melodica player notices any vibrato weirdness.

We looked at the situation where the mouthpiece was blocked and a note was played. What if someone is blowing and then plays? As I noted, a rigid air chamber could start out with higher pressures than one made from a bladder. If you start blowing quietly, though, the bladder will maintain the higher pressure longer than the rigid case. Perhaps this is needed to get the heavier reeds moving?

When you want a note to stop, you have two choices: lift the key or stop blowing. If you lift the key, rigid and bladder chambers should work identically. If you stop blowing but keep the key down, the note will have a longer decay with a bladder. Since most of us probably lift the key most of the time, the long decay is an effect we could avoid–unless we wanted it.

So my best guess now is that the bladder keeps more pressure on a reed for a longer period when it’s starting to sound. The degradation of the vibrato would just be an unfortunate side effect. It would also smooth out any transitions from quiet to loud (or vice versa), but if the smoothing function is not too long, it might not be noticeable (except on vibratos, of course).

The elasticity of the bladder control the smoothing. Making it stiffer or less stiff would probably change the behavior of the instrument. To pick the perfect material would require knowing a lot about the bass reeds and doing a lot of calculations–or using trial-and-error.

Again, this is just a hypothesis based on the little physics I know. Before I would accept my explanation as being accurate, I would want to run some real-world experiments. Things often prove to be more complicated than one expects.