sound velocity

[akimhaneul]

So it says in TBR that speed of sound in gas is square root (constant * pressure/ density).

I don't understand why speed would decrease with increase in density. I thought if density was higher, then the molecules would be closer together then collision and transfer of energy to occur faster? This would allow the sound wave to travel faster.

It says later in the book that the speed of sound is square root( restoring force/ molecular inertia). How is molecular inertia related to density?


Thank you!

---

Members don't see this ad.

 

[aldol16]

I don't understand why speed would decrease with increase in density. I thought if density was higher, then the molecules would be closer together then collision and transfer of energy to occur faster? This would allow the sound wave to travel faster.

The speed of sound depends not only on density but also on bulk modulus, which is basically how resistant something is to compression, or the restoring force that it will exhibit upon compression. So the higher the bulk modulus, the higher the restoring force, and the greater the impetus to transmit the sound on as vibrations. With most solids, the bulk modulus increases faster than the density so sound still travels faster in solids than liquids than gases.

So in other words, the molecules being close together doesn't matter if there is only a small force for that molecule to move and collide with something else. Imagine one billiard ball colliding with another. Billiard balls are fairly incompressible and energy is transferred from one to the other fairly quickly upon collision. The second ball then departs with most of the energy conserved. Now imagine two balls made of jello colliding. Jello is very compressible and so once they collide, energy transfer is slowed and damped by compression so that the second ball moves off much more slowly. Even if the jello balls were closer together to begin with, that effect is negated by their compressibility.

 

[wizzed101]

density = mass/volume = mole* Molar Mass/ Volume

Because gases more or less have the same volume at "normal" conditions when a gas has higher density it directly translates into higher molar mass and thus molecular size and weight. The latter dictates the inertia that impedes restoration forces.

The most salient point is, however, speed of sound depends solely on how fast can a cycle of compression and rarefaction complete.

And... that reasoning doesn't work for liquid and solid so in fact, that formula with P/rho only works for gases!

 

[BerkReviewTeach]

Great responses! In an oversimplified perspective, and building on wizard's input, as the molecules making up a gas get more massive (heavier), they move more slowly and cannot restore to their original position as quickly. This slows the longitudinal wave. So as whizzed points out, the mass factor in density is more significant than the volume factor. Also keep in mind that both density and pressure get reduced with increasing volume, so it is not very important in that equation.

 

[akimhaneul]

The speed of sound depends not only on density but also on bulk modulus, which is basically how resistant something is to compression, or the restoring force that it will exhibit upon compression. So the higher the bulk modulus, the higher the restoring force, and the greater the impetus to transmit the sound on as vibrations. With most solids, the bulk modulus increases faster than the density so sound still travels faster in solids than liquids than gases.

So in other words, the molecules being close together doesn't matter if there is only a small force for that molecule to move and collide with something else. Imagine one billiard ball colliding with another. Billiard balls are fairly incompressible and energy is transferred from one to the other fairly quickly upon collision. The second ball then departs with most of the energy conserved. Now imagine two balls made of jello colliding. Jello is very compressible and so once they collide, energy transfer is slowed and damped by compression so that the second ball moves off much more slowly. Even if the jello balls were closer together to begin with, that effect is negated by their compressibility.

Ok thank you! So what if you have a set of billiard balls that are close together and another set of billiard balls that are far apart? Since the first set has balls that are closer together (higher density than the second set), shouldn't sound propagate faster in the first set?

If this is true, then why is it that the formula for sound velocity is square root (bulk modulus/density)?

 

[BerkReviewTeach]

Bulk modulus has to do with solids, while the billiard ball example you are describing involves balls that are spread apart like gas particles. As such, you cannot apply the rules for a solid to the situation involving a gas. For bulk modulus to apply, the balls in your analogy have to be in contact.

In your original post, you are talking about the equation for speed of sound in a gas, which is based on gas pressure and gas density and has nothing to do with bulk modulus. Wizzed did a very good job explaining behavior in a gas and pointing out that those rules are not applicable to a liquid or a solid. Aldol16's explanation describes a solid and points out that with solids the bulk modulus has a strong correlation to restoring force.

 

[akimhaneul]

Bulk modulus has to do with solids, while the billiard ball example you are describing involves balls that are spread apart like gas particles. As such, you cannot apply the rules for a solid to the situation involving a gas. For bulk modulus to apply, the balls in your analogy have to be in contact.

In your original post, you are talking about the equation for speed of sound in a gas, which is based on gas pressure and gas density and has nothing to do with bulk modulus. Wizzed did a very good job explaining behavior in a gas and pointing out that those rules are not applicable to a liquid or a solid. Aldol16's explanation describes a solid and points out that with solids the bulk modulus has a strong correlation to restoring force.

Thank you. So does this mean that you don't use the formula square root (bulk modulus/density) for gas?


Sent from my iPhone using SDN mobile

 

[wizzed101]

Geezz... Let's try this.

Explain why does sound travel the fastest in solid, then liquid then gas, given that density of each respective state is in that order.

Edit: plz no formula

 

[akimhaneul]

Geezz... Let's try this.

Explain why does sound travel the fastest in solid, then liquid then gas, given that density of each respective state is in that order.

Edit: plz no formula

Because compared to gas, particles in solid and liquid have stronger bonds with each other and are less compressible, allowing them to move quickly and quickly allow the sound wave to propagate?





Sent from my iPhone using SDN mobile

 

[wizzed101]

Because compared to gas, particles in solid and liquid have stronger bonds with each other and are less compressible, allowing them to move quickly and quickly allow the sound wave to propagate?





Sent from my iPhone using SDN mobile

Are you sure about that?

Even then, how does their moving quickly help sound propagate?

 

[akimhaneul]

Are you sure about that?

Even then, how does their moving quickly help sound propagate?

Well sound wave movement involves moving of the particles, so if the particles are more free to move, they can propagate the wave faster.

particles can return to their original position faster and receive the next wave.


Sent from my iPhone using SDN mobile

 

[wizzed101]

But particles in solids are not free to move. In fact they are locked in lattices.

 

[akimhaneul]

But particles in solids are not free to move. In fact they are locked in lattices.

Hmmm...I guess I'm getting confused about this part.


But solids in general are incompressible compared to gas so when sound wave moves through, energy can be transferred much more efficiently.


Sent from my iPhone using SDN mobile

 

[wizzed101]

Okay