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
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.
I think this document 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:
It’s amazing how well this sentence holds up when taken out of context.
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.
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.
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.
When adding incoherent acoustic sources, the signal strength increases with the square root of the number of sources. So, instead of 10log10(N), we have 5log10(N).
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.
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:
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
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.
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.