# The Science of Sound **URL:** \ **Category:** Factual Questions\ **Created:** [September 3, 2009, 3:16am UTC](https://boards.straightdope.com/t/the-science-of-sound/508719 "2009-09-03T03:16:46Z")\ **Posts on this page:** 15\ **Page:** 1
**Author:** ![notfrommensa](https://avatars.discourse-cdn.com/v4/letter/n/f14d63/32.png) [@notfrommensa](https://boards.straightdope.com/u/notfrommensa)\ **Post date:** [September 3, 2009, 3:16am UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/1 "2009-09-03T03:16:46Z")
Question 1: Does sound travel more efficiently in less humid air? The other night, I was lying awake in the middle of the night, and a passing train tooted its horn. Many trains go through my town every day, but this time, the whistle seemed louder. Of course, it could have been a louder whistle but I also know that the weather had just broke and the air was considerably less humid, and the fact there was less moisture in the air might have made the decibel level higher. Or maybe it does, but the human ear is not calibrated enough to know the difference. TR, I live about 3/4 mile south of the RR tracks. Question 2: My local HS was playing their first football season of the year, about a mile west of my house. I could easily hear the PA system and faintly hear the cheers from my deck (enjoying an adult beverage or two). Obviously I cannot not hear anyone one person scream from that far away, but when several hundred (thousand?) people scream at the same time, it makes sense that I could hear them. But how are the sounds additive? One person screaming at 100 db doesn’t turn into 200 db level when the guy right next to him screams at 100 db? what about when 100 people scream at 100 db, or even a 1,000? I suspect the calculation use logarhithms but google skills are not very good. So I turned to the straight dope. Thanks in advance ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 3, 2009, 3:33am UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/2 "2009-09-03T03:33:19Z")
I do know that the decibel scale is logarithmic, though I couldn’t tell you the exact formula off the top of my head. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [September 3, 2009, 10:51am UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/3 "2009-09-03T10:51:01Z")
Sound amplitudes are additive, so you can get interference patterns from coherent sound sources, just like with coherent light sources. People yelling aren’t going to add coherently, though. As for adding noise levels, _decibels_ are tenths of Bells, and Bells are strictly logarithmic. So 2 Bells is _ten times_ 1 Bell, which means that 20 decibels is ten times 10 decibels. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [September 3, 2009, 11:54am UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/4 "2009-09-03T11:54:15Z")
I think [this document](http://www.mne.psu.edu/lamancusa/me458/10_osp.pdf) will tell you everything you need to know. Humidity play a role, but the bigger factor is the differing atmospheric temperature gradients during day and night, which work to either refract sound away from the ground (during the day), or refract it down toward the ground (at night). A relevant paragaph: > [@](#): > > In the presence of a temperature gradient, the effect is to refract sound waves in the direction of lower sound velocity (in this case, the lower temperature). Typical temperature profiles are shown in Figure 4. A common atmospheric occurrence is a negative temperature gradient (temperature decreases with altitude). This is typical of a sunny afternoon, when significant solar insolation causes high surface temperatures and significant heat transfer from the ground to the adjacent air. This event is also known in meteorological terms as a superadiabatic or positive lapse. In this situation, sound waves will be bent upward in all directions from the source, forming a circular shadow zone. The reverse situation often occurs at night, when a positive gradient is common. This is caused by the rapid cooling of air at the surface as heat is now absorbed by the ground. This is called an inversion or negative lapse and the sound waves are bent downward. This phenomena explains why sound sometimes travels much better at night, because it is focused along the ground instead of radiating upward. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [September 3, 2009, 1:10pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/5 "2009-09-03T13:10:05Z")
> [@CalMeacham](#): > > People yelling aren’t going to add coherently, though. It’s amazing how well this sentence holds up when taken out of context. > [@CalMeacham](#): > > As for adding noise levels, _decibels_ are tenths of Bells, and Bells are strictly logarithmic. So 2 Bells is _ten times_ 1 Bell, which means that 20 decibels is ten times 10 decibels. To put this another way, every doubling of the intensity of a sound corresponds to an increase of about 3 decibels. In particular, a thousand people shouting at once would be 30 decibels louder than one person shouting. ---
**Author:** ![Captain\_Awesome](https://avatars.discourse-cdn.com/v4/letter/c/a698b9/32.png) [@Captain\_Awesome](https://boards.straightdope.com/u/Captain_Awesome)\ **Post date:** [September 3, 2009, 1:50pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/6 "2009-09-03T13:50:30Z")
Contrary to what you might expect, sound travels faster in _more_ humid air, though as **Joe Frickin Friday** points out, this effect is fairly trivial. At 20°C, 1 atm, the increase in speed between 0% and 100% relative humidity is only 1.25 m/s. This increase is by virtue of the fact that water molecules are comparatively lighter than nitrogen and oxygen molecules, hence humid air is less dense. Sound travels faster in lower density mediums with all other things being equal. Adding two equidistant sound power sources, in harmony, both at 100 dB will produce a volume of 103 dB, or 120 dB with 100 sources, or 1,020 dB with 100 sources at 1,000 dB. > [@](#): > > ``` > Lwt = 10 log(n N / N[sub]0[/sub]) > = 10 log(N / N[sub]0[/sub]) + 10 log(n) > = Lws + 10 log(n) (1) > > where, > > Lwt = the total sound power level (dB) > Lws= sound power level from each single source (dB) > N = sound power (W) > N[sub]0[/sub] = 10[sup]-12[/sup] - reference sound power (W) > n = number of sources > > ``` [engineeringtoolbox.com](http://www.engineeringtoolbox.com/adding-decibel-d_63.html) Sound refraction due to temperature inversion or the effects of wind shear, if downwind of the source, have a more significant effect on audible volume. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [September 3, 2009, 3:52pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/7 "2009-09-03T15:52:04Z")
When adding incoherent acoustic sources, the signal strength increases with the square root of the number of sources. So, instead of 10_log10(N), we have 5_log10(N). ```auto Coh Incoh Num Sum Sum [dB] [dB] 1 0 0 2 3 1.5 3 5 2.5 5 7 3.5 10 10 5 20 13 6.5 30 15 7.5 50 17 8.5 100 20 10 1000 30 15 ``` ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [September 3, 2009, 5:13pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/8 "2009-09-03T17:13:29Z")
> [@Pleonast](#): > > When adding incoherent acoustic sources, the signal strength increases with the square root of the number of sources. So, instead of 10_log10(N), we have 5_log10(N). The amplitude of the signal increases as the square-root, but the intensity of the sound (in terms of power radiated) scales linearly. ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [September 3, 2009, 5:34pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/9 "2009-09-03T17:34:17Z")
> [@CalMeacham](#): > > _decibels_ are tenths of Bells, and Bells are strictly logarithmic. Note that, as the word “decibel” would suggest, the correct spelling is “bel”. [/nitpick] ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [September 3, 2009, 7:58pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/10 "2009-09-03T19:58:19Z")
Note also that human hearing is itself logarithmic, but with a different slope. A 10 dB increase is 10 times the sound intensity. A 10 dB increase is perceived to be about twice as loud. This logarithmic perception lets us hear things across 12+ orders of magnitude in sound intensity, and the rule-of-thumb scaling (about 2x louder for 10 dB increase) works pretty well across the whole audible range for people with normal hearing. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [September 3, 2009, 9:14pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/11 "2009-09-03T21:14:38Z")
> [@MikeS](#): > > The amplitude of the signal increases as the square-root, but the intensity of the sound (in terms of power radiated) scales linearly. I’m not sure how the amplitude scales, but the power radiated (which is what I meant by signal strength) definitely scales with square-root of the number of incoherent sources. If you know Matlab, try this simple calculation: ```auto a=randn(1e4,1e3); % create 1000 white-noise signals of 10000 samples each s=cumsum(a,2); % add up the signals--the Nth column has the sum of N sources p=sqrt(mean(s.^2)); % compute the RMS power of each column plot(1:1e3,p) % plots the power as function of number of summed sources ``` You’ll get a nice square-root curve. ---
**Author:** ![notfrommensa](https://avatars.discourse-cdn.com/v4/letter/n/f14d63/32.png) [@notfrommensa](https://boards.straightdope.com/u/notfrommensa)\ **Post date:** [September 3, 2009, 10:21pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/12 "2009-09-03T22:21:26Z")
Boy, am I sorry I asked. Some deep math, and it give me a headache. Anyways thanks for the responses. I got more than I bargained for. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 3, 2009, 10:39pm UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/13 "2009-09-03T22:39:56Z")
> [@](#): > > p=sqrt(mean(s.^2)); % compute the RMS power of each column If you’re looking at power radiated, which is proportional to intensity, you shouldn’t have that sqrt in there. ---
**Author:** ![Kevbo](https://avatars.discourse-cdn.com/v4/letter/k/e47774/32.png) [@Kevbo](https://boards.straightdope.com/u/Kevbo)\ **Post date:** [September 4, 2009, 3:06am UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/14 "2009-09-04T03:06:35Z")
Temperature inversions are common at the surface of a lake on a calm morning. It is not unusual to be able to hear fisherman talking in normal tones from a half mile or even more away. In this case, the inversion in the air refracts the sound down to the surface of the lake, which reflects it upward again giving a ducting effect. ---
**Author:** ![Uncertain](https://avatars.discourse-cdn.com/v4/letter/u/6a8cbe/32.png) [@Uncertain](https://boards.straightdope.com/u/Uncertain)\ **Post date:** [September 4, 2009, 3:46am UTC](https://boards.straightdope.com/t/the-science-of-sound/508719/15 "2009-09-04T03:46:33Z")
> [@Captain\_Awesome](#): > > This increase is by virtue of the fact that water molecules are comparatively lighter than nitrogen and oxygen molecules, hence humid air is less dense. Sound travels faster in lower density mediums with all other things being equal. Though it’s not density _per se_ that matters. For a given temperature, the speed of sound in a particular gas is approximately independent of pressure, and hence density. (I think that for an ideal gas the independence is exact.) However, as you say, lighter molecules make for faster propagation of sound. At a given temperature, lighter molecules have a faster average speed, since they have the same average kinetic energy. But sound will travel at about the same speed through high-density nitrogen as through low-density nitrogen, and will travel faster through high-density helium than through low-density nitrogen.