Doubts related to speed of sound in different mediums

since childhood we have been taught that sound travels faster in solid (most dense) as compared to liquids (less dense). and speed of sound is greater in liquids as compared to gases (least dense), sound can't travel in vacuum (0 density). and we were knowing the fact that speed of sound in moist air is more than dry air. and the reason we built was that more dense more speed. but recently i came to know that dry air is more dense than moist air .. why is this breaking the logic? pls help

It's to do with the fact that the dryness (humidity) of the air depends on temperature and the speed of sound in air also depends on temperature, see

https://www.nde-ed.org/Physics/Sound/tempandspeed.xhtml

which has this equation

$$v=331+0.6T$$

Dry air is typically at a lower temperature than humid air. So even though it may be more dense, the overall effect is that the speed of sound can be lower in dry air.

To imagine why warm air can hold more moisture than cold air - imagine a tray of water on a table in a cold room, not much water evaporates and is held by the air. In a warm room the water would quickly evaporate and be held by the air.

• The speed of sound in an ideal gas depends on its molecular weight. The MWs of oxygen (32) and nitrogen (28) are both significantly higher than water vapour (18) so the "MW of air" depends on the moisture content. Commented Mar 14, 2021 at 11:50
• thats right but i am taking temp. to be same .. as @alephzero said this is the reason given in my textbooks . so according to this more dense less speed and vice versa(indirectly related) ,.. so why is this not applicable in solids. solids are significantly denser than gas but velocity in solids travel faster (directly related since more density more speed of sound) i am confused Commented Mar 14, 2021 at 11:57
• i am studying speed of sound formula which was given by newton and corrected by laplace.. and i take temo to be same Commented Mar 14, 2021 at 11:58
• imgur.com/a/tM7sIoI (<--- see this) why is this fact in contrary ti the fact that speed of sound is most in solids(even though density is very high) Commented Mar 14, 2021 at 12:06

The speed of sound in an ideal gas is $$c = \sqrt{\frac{\gamma k T\strut}{m}}$$ where $$k$$ is Boltzmann's constant, $$T$$ is the absolute temperature, $$m$$ is the mass of one molecule of the gas, and $$\gamma$$ is the "adiabatic index" which depends on the number of internal modes of vibration of the molecule.

Dry air is mostly a mixture of oxygen ($$m = 32$$) and nitrogen ($$m = 28$$) using atomic weight units for $$m$$. Oxygen and nitrogen are both diatomic molecules, and $$\gamma = 1.4$$.

Water vapor has $$m = 18$$ and is triatomic, with the three atoms in the molecule not arranged in a straight line, and $$\gamma = 1.333$$.

At the same temperature, the speed of sound in each gas is therefore proportional to

Gas $$\sqrt{\gamma/m}$$
Oxygen 0.21
Nitrogen 0.22
Water vapor 0.27

so the speed of sound in a mixture of the three gases (i.e. "air") is higher as the water vapor content increases.

The speed of sound is given by : $$\sqrt{\dfrac{B}{\rho}}$$.

$$\rho$$ is the density and B is the bulk modulus of elasticity.

The speed of sound is higher for moist air since its density is lower. This is because the speed does depend inversely on the square root of the density.

The speed of sound for liquids in general is higher than it is for gases because the elasticity of liquids (Bulk Modulus) is higher.

A liquid has a higher elasticity since it is difficult to compress compared to a gas.

To get a comparison of the numbers involved, The bulk modulus of air ranges from about $$\sim$$ 1-1.5 $$\times 10^5$$ Pascal, and the bulk modulus of water is $$\sim$$ 2 $$\times10^9$$Pascal

so the ratio of the bulk modulus of water to that of air $$\dfrac{B_{water}}{B_{air}}$$is atleast 10000.

The density of water is $$\sim$$ 1000 kg/m^3 and the density of air is $$\sim$$ 1 $$kg/m^3$$ and so the density of air (dry/moist) is about 1000 times smaller than the density of water. i.e $$\dfrac{\rho_{water}}{\rho_{air}}$$ $$\sim$$ 1000.

Since the ratio $$\dfrac{B_{water}}{B_{air}} > \dfrac{\rho_{water}}{\rho_{air}}$$, the speed of sound in water is greater than that in air.

It's actually a common myth that density is responsible for the speed of sound in a medium. The belief is that the speed of sound is higher in more dense mediums, and slower in less dense mediums. If this is the case, why is the speed of sound faster in less dense helium gas than it is in air?

Popular science YouTuber Cody'sLab explained how the speed of sound works in his video Thunderground 2: Artificial Thunder (explanation starts at 4:56). To summarize his points, he explained that the speed of sound actually depends on the strength of the intermolecular bonds of the material. For a sound wave to propagate, the atoms must be displaced, and then return to their original position. If they don't return, the energy is absorbed and the wave stops. The faster and more efficiently they return (via the pull of stronger intermolecular bonds), the faster the propagation of energy and therefore speed of sound is.

It's generally true that solids have stronger intermolecular bonds than liquids which have stronger ones than gases, which is why the speed of sound approximately correlates with density. It's not a direct causation though, as the helium example demonstrates.