speed of sound question

[LetsGo352]

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The BR physics book states that the speed of sound:

v=sqrt((k)(P/d))

where k=constant
P=pressure of medium
d=density of medium.

This would imply that larger densitites will result in lower sound velocity. But how does sound travel in mercury faster than it travels in water when mercury has the the larger density?

 

[unique135]

Speed of sound in water is 1493 m/s and in mercury is 1450 m/s at 25C.

 

[LetsGo352]

Speed of sound in water is 1493 m/s and in mercury is 1450 m/s at 25C.

I guess BR book is wrong? Here is a direct quote from BR physics part 2 p.39:

"Just like sound intensity, the speed of sound also increases as a medium becomes denser. If we are looking for the medium in which the speed of sound is slowest, we would be looking for the medium of least density."

 

[unique135]

I guess BR book is wrong? Here is a direct quote from BR physics part 2 p.39:

"Just like sound intensity, the speed of sound also increases as a medium becomes denser. If we are looking for the medium in which the speed of sound is slowest, we would be looking for the medium of least density."

This seems contradictory.

Speed of sound in a medium depends on two properties of the medium.
1. Elasticity (Stiffness/Change in shape)
2. Inertia (Density/Change in motion)
Plus Temperature

Denser mediums slow down the speed of sound while stiffer mediums speed up the speed. There is competition between these two.
Water is denser than air, yet water's speed of sound is high. This is because, a little change in pressure changes volume largely in air (representing low Bulk Modulus); but water has larger bulk modulus. Stiffness or bulk modulus wins over density; water has high speed of sound.


For speed of sound comparisons,
Mercury vs. Water:
Mercury is denser than water. ----> favors water
Mercury is stiffer than water? ----> I don't know. Even if it is, I doubt it will win over density.
Density wins. Water has higher speed of sound.

Water vs. Wood:
Water is denser than wood. ----> favors wood
Wood is much stiffer than water.----> favors wood
Both wins. Wood has higher speed of sound.

Wood vs. Aluminum:
Aluminum is denser than wood. ----> favors wood
Aluminum is much stiffer than wood. ----> favor aluminum
Stiffness wins. Aluminum has higher speed of sound.


Aluminum vs. Steel:
Steel is denser than aluminum. ----> favors aluminum
Steel is much stiffer than aluminum ----> favor steel
Stiffness wins again. Steel has higher speed of sound.

 

[BerkReviewTeach]

The BR physics book states that the speed of sound:

v=sqrt((k)(P/d))

where k=constant
P=pressure of medium
d=density of medium.

This would imply that larger densitites will result in lower sound velocity. But how does sound travel in mercury faster than it travels in water when mercury has the the larger density?

That equation applies to gases, which unfortunately the book doesn't mention until the paragraph after the equation where is defines the Cp and Cv values as applying to a gas.

So while it's not a typo per say, it failed to mention that it applies to gases.

 

[BerkReviewTeach]

I guess BR book is wrong? Here is a direct quote from BR physics part 2 p.39:

"Just like sound intensity, the speed of sound also increases as a medium becomes denser. If we are looking for the medium in which the speed of sound is slowest, we would be looking for the medium of least density."

That direct quote is not a general statement, but part of an answer explanation to the following question.

• The SLOWEST measurable speed for a propogated sound wave is observed in which medium?
  A. A vacuum
  B. Air
  C. Fresh water
  D. Salt water

In the context of this question, you should eliminate vacuum immediately, because sound requires a medium for propogation. When considering the reamining three choices, it comes down to how quickly the particles of the medium can collide with a neighboring particle and restore back to their original position. The ability to do this is greatest in the densest medium of the choices given. This means that the slowest speed will be observed in the gas, and not a liquid. You might also know that the speed of sound in air is about 340 m/s (depending on temperature and pressure) and about 1500 m/s in fresh water. The bottom line is that you should take answer explanations in the context of the question they are associated with, and not necessarily as universal truths.

 

[LetsGo352]

So is there a general for speed of sound in other media besides gases? Or do we just have to know the general relationships (like the poster above explained with elasticity and density)?

Thanks for the help.

 

[kentavr]

So is there a general for speed of sound in other media besides gases? Or do we just have to know the general relationships (like the poster above explained with elasticity and density)?

Thanks for the help.

There is, but it is beyond MCAT, I hope. The propagation of sound wave in the media can be modeled (in 1-dimensional case) using spring and mass. F=-kx and F=ma.
And the model looks like ...---Msas---Mass---Mass---... That's why two parameters are important: density and elasticity. For ideal gas the oscillation equation based on this model can be solved and wave speed can be estimated. For liquids it become more complicated and for solid due to the crystal structure it become very(very) complicated. HTH