# Speed Of Sound...

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#### Biffer

##### The good times doc
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I am somewhat confused about the speed of sound..since two of my prep books (jump start MCAT and FlowerSilver) offer contradicting explanations! haha. Instead of reviewing my textbook I felt like posting--in order to help you too.

does velocity of sound increases with increasing density? I know the modulus increase is directly proportional to v.. but is density as well. it makes sense that if the material is more dense it will convey sound slower due to shorter wavelength..right? confusion sets in..

please clarify these terms since my books have failed me,
biffer

#### Mike59

##### Sweatshop FP in Ontario
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Remember it like this:

Sound travels fastest in a solid, then in a liquid, and slowest in gas. It is a longitudinal wave, therefore the denser medium vibrating will allow for better transmission of the wave. Therefore, sound speed varies proportionally with density. Don't worry about wavelength in this case.

Good Luck!

#### Mr. Z

##### Senior Member
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The velocity of sound is decreased by more dense mediums. This is due to the mediums inertial component. The wave must move the medium to propagate, therefore a heavier medium will be more difficult to move than a lighter, slowing it down.

However, an increasing elastic component of the medium will tend to speed up the wave. This is because a medium with a higher elastic component will return to its undisturbed state faster than a medium with a lesser elastic component.

#### Mike59

##### Sweatshop FP in Ontario
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Mr. Z, I must disagree with your statement regarding velocity vs. density. For the same reason that the velocity of sound is 0 m/s in a vacuum, it increases proportionally with increasing density.

#### Biffer

##### The good times doc
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is this right--- v= sqroot(B/density) ?
B=bulk modulus.

#### Biffer

##### The good times doc
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If the above eq is correct then the Z-man is right. Intuitively though, I would have thought that when the density increases--the distance between each rarefaction + compression decreases and so v=lamb * f applies.. = greater velocity?

#### Biffer

##### The good times doc
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my bad-- the correlation is right-and the velocity decreases with greater rarefaction/compression... its getting late.

#### Mr. Z

##### Senior Member
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Actually, i made a mistake. Let me clarify it...

You can't determine the relative velocity of a sound wave in a medium based on density alone. You must include the
elastic component (bulk modulus) of the medium in your comparison.

My bad. cut me some slack it's late... i'm going to bed

#### freakazoid

##### Guy Friend Extraordinaire
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Is warmer air less dense, and therefore sound travels slower?

#### Mr. Z

##### Senior Member
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freak,

for a gas, the velocity of sound is directly proportional to the temperature of the gas.

the equation v= (yRT/M)^1/2

y (really it's gamma) is a constant
R is the universal gas constant
T temperature
M molecular mass

#### freakazoid

##### Guy Friend Extraordinaire
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I stand corrected. Thanks Z.

#### Mr. Z

##### Senior Member
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No, its not important to know that equation. I just put it in the post so people would know I wasn't pulling stuff out of my butt.

Just know that velocity of sound in a gas is directly proportional to the temperature of the gas.