Why will two equal sounds travel further than 1 of the same sound. I have a race track about 5 miles from my house and on race night it sounds like it is right next door. The high school is maybe 1 mile away and on football night I can hear them cheering as if they are right next door. Also is this affect the same with high or low frequecies?
Sure. If you have two things making a sound of a certain loudness it will be twice as loud as if there were only one of them, and thus, other things being equal, you will be able to hear it twice as far away.
This was asked, though without definitive answer, in a two years-ago thread. zombywoof mentioned that “Reportedly the 1883 Eruption of Krakatoa was heard 2200-3000 miles away.”
A complication is that there are (at least) two major causes of sound reduction over distance: scattering and absorption. The former follows an inverse-square-distance law, the latter an inverse-distance law.
In the above thread John Mace provided a link to a Javascript that calculates sound attenuation. At that page, you can type in air temperature, sound frequency, etc. to get “sound reduction in dB per km.” Is that result intended to be indeed a constant? If so, that seems to imply they consider only absorption, not scattering.
Sound intensity is generally measured in decibels, but this logarithmic measure can be confusing. Two 40 decibel sources combine to give 43 decibels; two 60 decibel sources yield 63 decibels, etc. (However human nervous system applies its own non-linearities so it takes a 10-decibel difference to “seem twice as loud.”)
In addition, the inverse-square law for spherical radiation has a coefficient of 1/4 (for a full sphere, 1/2 for a hemisphere). The coefficient for deterioration per mile for absorption is tiny in comparison, so the radiation aspect dominates.
“Twice as loud” is subjective, and while 10 dB is often used as a rule of thumb, some people report 6dB as twice as loud. 6dB is twice the amplitude, 4 times the power. 10dB is 10 times the power (pretty much by definition, I believe).
When two signals are added together, if they’re the same signal, in phase, the result is 6dB: twice the amplitude, 4 times the power. If the two signals are totally uncorrelated, the result is 3dB louder, twice the power.
So, in the case of cars or spectators, with two of them we get only a 3dB increase rather than a 6dB or 10 dB increase (twice as loud). But njtt is still correct in principle, that as you add more, it gets louder, and if it’s louder at the source, it’s the same amount louder (in dB) anywhere you measure it.
I also don’t think that a sound that’s twice as loud (by either definition) travels twice as far, but it definitely travels farther.
Opps, made some mistakes above. The bit about “twice as loud” is correct, but ignore the rest.
I think absorption, reflection and wind speed would all be significant factors. I assume absorption is the main factor as to why lower frequency sounds travel further.
Phase I don’t think is massively important in practice, simply because you’ll get an averaging effect due to reflections of the original sound waves
I agree with the answers above and would like to add…
You may be the unfortunate recipient of a little building “amplification”. Some structures act like a megaphone, while not actually amplifying they concentrate reflections and send them out in specific directions. IME stadiums and grandstands can do this. Geographic features like hills and valleys can do this as well. Hope this does not annoy you too much.
Capt
I looked at the calculator. Since it’s measuring sound pressure level in dB, and it’s dB per mile, it is taking the inverse square law into effect. See the section on acoustics in the wiki: Inverse-square law - Wikipedia
So, forget what I said about what factor dominates, because the calculator includes both effects (dispersion and absorption).
In general there’s a third factor that we use for evaluating loudspeakers for PAs (like, for rock bands), which is dispersion angle. The lower the angles (we usually get two numbers, vertical and horizontal), the “longer the throw”, so coverage is a narrower region but deeper penetration. That effects the coefficient I mentioned above. Note that I’m a hobbyist in PA applications, and I haven’t actually done the math.
So, I was correct above about addign signals together (correlated vs. uncorrelated). I wasn’t sure about correcting njtt on the “twice as far” part, but I think I was right after all.
If the decrease is dB per distance, and a fixed number of dB increase is “twice as loud”, then a signal that’s twice as loud would travel a fixed number more miles than the quieter one before reaching the same SPL (sound pressure level).
For example, according to the calculator posted above and using default values, 565 Hz degrades at about 3 dB/mi. Let’s assume that 6dB is “twice as loud”. So, a signal that’s twice as loud would be 6dB higher and would go 2 mi farther before being attenuated as much as the original signal at the original distance.
Regarding wind speed, if it’s laminar, just use it to compensate for distance.
If it’s turbulent, I suspect it would degrade things more, but hard to say how much.
Regarding phase, that’s subsumed by what I said about correlated versus uncorrelated noise: the result is between 3dB and 6dB depending on correlation (or down to 0dB for negative correlation). 3dB is the equivalent to the standard math for adding noise factors, where the sum is the square root of the sum of the squares. Also, for the math, we’re assuming a flat surface (the ground) and no obstructions or reflections.
Absorption is definitely the reason low frequencies travel farther. The high frequencies filter out. If the medium was a tube rather than a hemisphere, you’d use the math for a transmission line.
The atmosphere can greatly affect how far sound travels. Sound speed depends on temperature. You’ve probably seen the effect where a warm road far ahead looks wet, and reflects the sky. A similar effect can happen in the air, if sound travels faster at higher elevation, refracting the sound back down to the ground.
I live about 5 miles from the University of Michigan football stadium. I usually don’t hear it, but one warm day, I could hear the cheers every time there was a big play. It was kind of neat. I’d see the play on TV, watch a replay of it, then mosey out to my front porch and hear the cheers 20 or 30 seconds later. Only that one day, though.
Wind can do this as well. Wind speed generally increases away from the ground. If the high school and track are upwind of you, the effect of greater wind speed at higher elevation will also tend to refract the sound back down to the ground, instead of allowing it to continue upwards. If the prevailing winds come from this direction, you may hear this often.
This is a case of atmospheric refraction, and is associated with thermal inversions, which by definition are an unusual thing. I get the same thing at my house: most days I can’t hear the highway a mile away, but some days it’s exceptionally noisy.
I live about 8 blocks from the busiest freeway in the US. They have a 10 foot block wall on the sides which effectively stops any noise from reaching me. On a few occassions I have had days where I could hear the freeway.