Why does sound travel faster in helium that is lighter than air but also travels faster in water that is more dense than air?
In: Physics
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The speed of sound is related to the speed at which the molecules move, as it is the molecules bumping into each other that allows the pressure wave to propagate. The speed of the molecules depends on the temperature and the mass of the molecule. Temperature is the energy the molecules have, and for a given amount of energy, something lighter moves faster than something heavier.
Air is mostly nitrogen and oxygen, which are formed of diatomic molecules, so one nitrogen molecule has two atoms, same for oxygen. Oxygen has a mass of 16 and nitrogen 14 per atom, so air is composed of molecules of mass 28 (a bit above 70%) or 32 (most of the rest). Helium atoms have a mass of 4, and don’t form molecules. Water is 1 oxygen and two hydrogen (mass 1 each), so a water molecule has a mass of 18.
The speed of sound (c) in gases is depends on two things:
– density (rho)
– bulk modulus (K)
by the equation:
c = sqrt(K/rho)
The bulk modulus tells you how much pressure you need to compress a gas – or vice versa, how much compression you need to transmit pressure. I think its kind of intuitive that a gas that only needs to compress a little bit transmit pressure faster thab one that has to compress a lot.
If you think about it this way. Air is mostly nitrogen and oxygen which are both heavier elements than helium. So getting air to move a certain way is going to take more energy to get things going and will also be slower in doing it. It’s exactly like if you push on a car, it’s not going to move much but if you push on a ball it’ll roll away from you easily.
For water, the atoms are all packed in together and all but touching. The moment you hit one water molecule, the energy quickly transfers to the next because it doesn’t have far to go to do it.
For another example, think about a game of billiards. Except at the start you line all the balls up in a straight row touching each other down the length of the table. Hit one end of the row and the ball at the other end pops off almost immediately. That’s how water do.
Now put an inch or two between each of the balls in that same kind of line and when you smack one end it takes a few seconds before the ball at the other end starts to roll. That’s how gas do. (In this case water vapor)
If you replaced the billiard balls with say squash balls or tennis balls, it should take a little less time for the far end to get moving because there’s less momentum to overcome for each ball in the chain. That’s how it looks for any gas lighter than water in gas form. Which is similar to how helium is “lighter” (less massive) than air.
I am confident that my research into the op subject matter is factual. That I lack a complete understanding of the subject is not pertinent to the discussion.
Furthermore there was no ‘guess work’ involved.
Please refer to the following links.
[speed of sound through helium ](http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/souspe.html#:~:text=Sound%20Speed%20in%20Helium.%20The%20speed%20of%20sound,is%20so%20much%20less%20than%20that%20of%20air.)
Speed of sound through water.
[speed of sound through water](https://hypertextbook.com/facts/2000/NickyDu.shtml#:~:text=The%20speed%20of%20sound%20can%20also%20be%20affected,water%20at%20room%20temperatures%20%2820%20to%2025%20%C2%B0C%29.)
[thermal conductivity of gases](https://www.engineersedge.com/heat_transfer/thermal-conductivity-gases.htm#:~:text=%20%20%20Gas%20%20%20Temperature%20%C2%B0C,x%2010%20-6%20%2019%20more%20rows%20)
[can sound generate heat? ](https://wtamu.edu/~cbaird/sq/mobile/2015/11/05/can-sound-waves-generate-heat/)
Following the above links we can see that temperature and pressure both affect the ability of sound to travel through a given medium. In our case air/helium/water.
Since sound waves are a form of mechanical energy they are governed by the laws of thermal dynamics.
[fundamentals of sound](https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9B__Waves_Sound_Optics_Thermodynamics_and_Fluids/02%3A_Sound/2.01%3A_Fundamentals_of_Sound)
As I stated, I have researched the topic, declared that I was not an expert. In fact I stated I was a layperson, which is very clearly stated that I should do in the rule cited as the reason for my post removal.
These above links clearly hold that my post was indeed accurate in that the reason sound travels faster in helium than air is because helium is far more energetic as a medium and sound waves are governed by thermal dynamics.
Thank you in advance for your consideration in the restoration of my post.
I am still learning the nuances of ELI5.
I felt that a more verbose reply would be unhelpful in answering the question as asked.
Sound is a physical pressure wave of particles. They act like little balls – one knocks the one beside it, which hits the one beside it, on and on, until one hits your ear drum. It’s like ripples in a pond. The “speed of sound” is how fast these ripples move along. It has to do with how heavy the particles are, and how close together they are.
**Case 1: helium vs air** – As long as they’re at the same pressure and temp, all gases have the same density of particles. If you have a balloon of helium and a balloon of air, the He atoms in one are the same distance apart as the “air atoms” (N2 and O2) in the other. All things are equal in this comparison *except the mass of each single particle*. He is MUCH lighter than O2 and N2, so when you give them the same push they’re able to move along knocking into each other more quickly.
**Case 2: Air vs water** – Now the biggest difference is the distance between particles. In liquids (and solids), the particles are packed MUCH closer together than they are in gases. The speed of sound is much higher in liquids and solids because of this. Each ball has a very very short distance to go before hitting the one next to it so the wave moves quickly. Imagine pool balls lined up touching each other. Hit one end and one flies off the other end of the line almost immediately. Also single water molecules are somewhat lighter than air molecules, so it has a double-advantage.
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