# Speed of sound - paradox? **URL:** \ **Category:** Factual Questions\ **Created:** [February 8, 2006, 3:42am UTC](https://boards.straightdope.com/t/speed-of-sound-paradox/343498 "2006-02-08T03:42:14Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [February 8, 2006, 3:42am UTC](https://boards.straightdope.com/t/speed-of-sound-paradox/343498/1 "2006-02-08T03:42:14Z")
Sound travels faster in dense materials since the atoms are more closely packed together - the medium to propogate the wave. However, cooler air is more dense than warmer air; yet, air travels faster in warmer air. What explains this apparent paradox? Should it matter that one medium is solid vs. gas? I have to run some number crunching about air at different temps to verify, but let’s assume the air pressure remains constant. (Unless this assumption precludes the above results from being possible.) - Jinx 😕 ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [February 8, 2006, 3:46am UTC](https://boards.straightdope.com/t/speed-of-sound-paradox/343498/2 "2006-02-08T03:46:37Z")
Consider the amount of motion of the air molecules as temperature increases. ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [February 8, 2006, 4:15am UTC](https://boards.straightdope.com/t/speed-of-sound-paradox/343498/3 "2006-02-08T04:15:11Z")
> [@Jinx](#): > > Sound travels faster in dense materials since the atoms are more closely packed together - the medium to propogate the wave. However, cooler air is more dense than warmer air; yet, air travels faster in warmer air. What explains this apparent paradox? Should it matter that one medium is solid vs. gas? > > I have to run some number crunching about air at different temps to verify, but let’s assume the air pressure remains constant. (Unless this assumption precludes the above results from being possible.) - Jinx 😕 I found the speed of sound in an ideal gas is: V = sqrt(d_r_t/m) where d is adiabatic constant r is gas constant t is absolute temperature m is molecular mass of gas So the warmer the gas, the faster sound is in it. This also explains squeaky-voice-syndrome with helium. Its molecular mass is less, so everything else being equal makes the speed of sound faster in it. If it’s the gas that’s filling your lungs and throat, your voice is going faster and makes your pitch go up. ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [February 8, 2006, 2:40pm UTC](https://boards.straightdope.com/t/speed-of-sound-paradox/343498/4 "2006-02-08T14:40:00Z")
> [@Jinx](#): > > Sound travels faster in dense materials since the atoms are more closely packed together - the medium to propogate the wave. However, cooler air is more dense than warmer air; yet, air travels faster in warmer air. What explains this apparent paradox? Actually, sound travels more slowly in dense materials. The hitch is that denser materials are usually _much_ stiffer, and that overcomes the retardation of the increased density. Speed of sound =K (stiffness/density)[sup]1/2[/sup] ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [February 8, 2006, 2:44pm UTC](https://boards.straightdope.com/t/speed-of-sound-paradox/343498/5 "2006-02-08T14:44:00Z")
That’s the relationship for solids, of course. My brother and I were discussing this very thing yesterday. It’s funny how often the Straight Dope chases up our conversations. I always thought of it as a result of how fast the molecules in the gas were moving. The faster they are moving, the faster they can communicate any disturbance to their neighbors. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [February 10, 2006, 4:05am UTC](https://boards.straightdope.com/t/speed-of-sound-paradox/343498/6 "2006-02-10T04:05:37Z")
> [@MonkeyMensch](#): > > Actually, sound travels more slowly in dense materials. The hitch is that denser materials are usually _much_ stiffer, and that overcomes the retardation of the increased density. > > Speed of sound =K (stiffness/density)[sup]1/2[/sup] Yes, I found this general equation in my Gas Dynamics book. It explains, that for ideal gases, the collisions between molecules is isentropic which allows other gas properties to stay constant. Because of this, it can be shown that the density doesn’t matter and the above equation can be manipulated to (almost) become the equation posted above by AWB. My equation applies “k” the ratio of the specific heats for any given gas. It is not as intuitive as people try to theorize (as seen in posts above)…