At this point, I’m thinking that a decrease in density does not decrease the speed of sound in gases, only in liquids and solids.
Actually, a decrease in density increases speed of sound in liquids and solids. (intuition: less mass → less inertia, faster movement for same forces). The same also does apply to gases (depending on what else is held constant, but consider, e.g. helium).
And, in the case of a gas, it’s not clear to me that, other things being equal, moving farther before hitting another particle should be expected to decrease the speed of sound. After all, even if it takes a longer time for a particle to hit another particle, it’s traveling farther in that time, so the total distance per time isn’t dropping.
Here is my synthesis of what happened: in solids and liquids, density does affect the speed of sound, but in gases, a third factor is pressure. If you increase the temperature, density can increase, but pressure also increases by a portional amount since the molecules are hitting harder. These two changes cancel out. Thus, in a gas v∝√T only.
It’s confusing to me here what you are assumptions you are making about what else is happening as the temperature changes. E.g. mentioning both pressure and density changing rules out both constant pressure and constant volume. Also, you mention density increasing instead of decreasing, which might be a typo?
Constant volume case: as the temperature increases, the density stays the same but the forces increase due to the increase in pressure, so sound moves faster.
Constant pressure case: as the temperature increases, the forces stay the same (since we’re holding the pressure constant), but the density (and hence inertia) decreases, so sound moves faster.
Good for you to be thinking about improving your understanding, best of luck in building up a strong physical intuition.
Actually, a decrease in density increases speed of sound in liquids and solids. (intuition: less mass → less inertia, faster movement for same forces). The same also does apply to gases (depending on what else is held constant, but consider, e.g. helium).
And, in the case of a gas, it’s not clear to me that, other things being equal, moving farther before hitting another particle should be expected to decrease the speed of sound. After all, even if it takes a longer time for a particle to hit another particle, it’s traveling farther in that time, so the total distance per time isn’t dropping.
It’s confusing to me here what you are assumptions you are making about what else is happening as the temperature changes. E.g. mentioning both pressure and density changing rules out both constant pressure and constant volume. Also, you mention density increasing instead of decreasing, which might be a typo?
One potential way to think about it, if you want to think in terms of pressure and density: (for actual math, see e.g. https://en.wikipedia.org/wiki/Bulk_modulus)
Constant volume case: as the temperature increases, the density stays the same but the forces increase due to the increase in pressure, so sound moves faster.
Constant pressure case: as the temperature increases, the forces stay the same (since we’re holding the pressure constant), but the density (and hence inertia) decreases, so sound moves faster.
Good for you to be thinking about improving your understanding, best of luck in building up a strong physical intuition.