Sound/Light Waves

[docntrainin]

---

Members don't see this ad.

Hi guys, I tried to find a clear answer for this question but I'm still confused. I read somewhere that the speed of sound increases in a dense medium (example was glass in comparison to air). Then, I also read somewhere that the speed of sound travels faster in less dense conditions i.e. hot air vs. cold air, sound will travel faster in the hot air. What is the relationship between speed of a sound wave and density? Also, what is the relationship between speed of a light wave and density? I think AAMC 7 confused me. Thanks.

 

[docntrainin]

As I'm waiting for a response, I have continued to think about this question. Should I just accept that sound travels faster in solids, but when thinking of a fluid (gas or liquid), sound will travel faster through the less dense medium, for example hot air in comparison to cool air.

Bump... this question has really been bugging me.

 

[Nkeflin]

in general, speed of a soundwave decreases with density (newton/laplace equation: c = sqrt(stiffness/density)). thus, sound travels faster through warmer air (less dense) than colder air (more dense)

the reason it increases as you increase the density of the medium (gas --> liquid --> solid) is because the stiffness (bulk modulus) of the medium increases at a greater rate. i wouldn't imagine we would have to know this equation for test day, but it's a good way to see the relationship.

light travels slower through a denser medium, hence, index of refraction. also, we tend to use the highest value for the speed of light in our calculations... SOL in a vacuum

hope this helps. sorry for all the parentheses. check out wikipedia if you're still confused

 

[Bumbl3b33]

in general, speed of a soundwave decreases with density (newton/laplace equation: c = sqrt(stiffness/density)). thus, sound travels faster through warmer air (less dense) than colder air (more dense)

the reason it increases as you increase the density of the medium (gas --> liquid --> solid) is because the stiffness (bulk modulus) of the medium increases at a greater rate. i wouldn't imagine we would have to know this equation for test day, but it's a good way to see the relationship.

light travels slower through a denser medium, hence, index of refraction. also, we tend to use the highest value for the speed of light in our calculations... SOL in a vacuum

hope this helps. sorry for all the parentheses. check out wikipedia if you're still confused

That's just confusing and over the scope of the MCAT in my opinion. Just remember that sound travels faster in a denser objects (think of extremes--if, with you ear against the wall, you pimp smacked a ho against a wall, can you hear it in the wall? Yes. If you pimp smacked her in a vacuum, could you hear her? NOPE! Sound is a longitudinal wave meaning it has to move atoms out of its way to produce a wave...if there's nothing there, like in a vacuum, no wave is propagated...but if plenty of stuff is there, increased density/solids, it moves bloody well!

 

[docntrainin]

haha thank you

 

[Nkeflin]

That's just confusing and over the scope of the MCAT in my opinion. Just remember that sound travels faster in a denser objects (think of extremes--if, with you ear against the wall, you pimp smacked a ho against a wall, can you hear it in the wall? Yes. If you pimp smacked her in a vacuum, could you hear her? NOPE! Sound is a longitudinal wave meaning it has to move atoms out of its way to produce a wave...if there's nothing there, like in a vacuum, no wave is propagated...but if plenty of stuff is there, increased density/solids, it moves bloody well!

... exactly why I stated that we probably don't need to know the equation for test day. I like to see mathematical relationships when I review concepts, so I figured it'd be helpful to show it to someone struggling with the relationship.

On another note, +1 for your example

 

[MT Headed]

Just remember that sound travels faster in a denser objects

No. Given two media that are alike in every other respect, sound travels slower in the denser medium. For the exact reason that a wave travels slower down a heavy rope than a light string.

The MCAT is notorious for trapping students that don't understand these subtleties.

 

[liveoak]

the bulk modulus is a bigger deal than density, thus it takes precedence over all.

 

[costales]

The speed of sound varies as the square root of the ratio of the "elastic properties"/"bulk properties". Think of sound propagating like a sling shot. The "stronger" the rubber band (restoring force) and the lighter the stone ("bulk property"), the faster the stone will travel when the stone is released.

 

[Bumbl3b33]

No. Given two media that are alike in every other respect, sound travels slower in the denser medium. For the exact reason that a wave travels slower down a heavy rope than a light string.

The MCAT is notorious for trapping students that don't understand these subtleties.

Can you expand on this? I'm afraid I don't understand.

Sorry if I confused you, OP!

Edit: Nevermind, makes sense.

 

[destroyMCAT]

lol I don't understand

 

[docntrainin]

haha wow good to know that i wasn't the only one confused about this!

so here is what i took from all of this:

if bulk modulus factor is the same, the less dense object is favored i.e. speed is faster. however, if bulk modulus is not the same, the one with the greater value will have sound travel faster. is this correct?

 

[MT Headed]

haha wow good to know that i wasn't the only one confused about this!

so here is what i took from all of this:

if bulk modulus factor is the same, the less dense object is favored i.e. speed is faster. however, if bulk modulus is not the same, the one with the greater value will have sound travel faster. is this correct?

Your second scenario depends on how much the density changed (if at all). Usually the bulk modulus is the more important of the two factors, so you'd be correct. Keep in mind that if the bulk modulus went up by a factor of 2 and the density went up by a factor of 4, then the speed would still be faster in the less dense object. velocity = sqrt(modulus/density).


Now you are ready for questions of this type:
The speed of sound in dry air is 343m/s
The speed of sound in air with 25% humidity is (greater/lesser/same/can't be determined)

Answer:
Air with water moisture in it is less dense than pure dry air (compare water's 18g/mol vs nitrogen's 28g/mol), therefore the speed of sound in moist air is faster than the speed of sound in dry air.

 

[gabdolce]

Wow, what a tricky question.

I had envisioned that the water filled air presented an impurity and consequently be more dense...