# Topic: Does the amplitude of a sound double when stacked?

1. ## Does the amplitude of a sound double when stacked?

Got involved in this question with a student, an old question I'm still not sure I really understand the answer to: does a sound, if duplicated, and heard at the same time as the original, create an exact doubling of volume? In other words, does amplitude stack in a neat simple way--does a 5 decibel sound, duplicated, give you 10 decibels? So sound is like water--pour a gallon of water into another gallon and you have two gallons? Or would you have only two five decibel sounds that are perceived as louder? (Is there a standard fomula, here?)

If they stack neatly, how is it possible for us to stand in a crowed theater, surrounded by applause, and not be deafened? Do the bodies and seating absord the sound? Is the variation in the pitches of each clap a reason for no doubling of volume with each additional person? Or for that matter, how can we sit at a piano and bear the sound of five notes played at an equal volume--if all the notes were at the same pitch, would the sound be deafening?

2. ## Re: Does the amplitude of a sound double when stacked?

it does double, but the dB doesn't double.

50 dB is quite a low volume. Twice as loud as 50 dB is..........hold on.....no, not 100 dB but .............56 dB. Basically 6 dB is a doubling in volume. Very strange scale, that dB scale. 30 dB you almost can't hear and 140 dB could make you deaf.

In regards to the crowd I'd say, not all 1000 people clap at the EXACT same time and most of them are so far away from you that the volume they produce TO YOU is probably less than 1 dB.

Actually I'm a bit confused myself now. I hope somebody can explain it further.

3. ## Re: Does the amplitude of a sound double when stacked?

Originally Posted by Jake Johnson
Got involved in this question with a student, an old question I'm still not sure I really understand the answer to: does a sound, if duplicated, and heard at the same time as the original, create an exact doubling of volume? In other words, does amplitude stack in a neat simple way--does a 5 decibel sound, duplicated, give you 10 decibels? So sound is like water--pour a gallon of water into another gallon and you have two gallons? Or would you have only two five decibel sounds that are perceived as louder? (Is there a standard fomula, here?)

If they stack neatly, how is it possible for us to stand in a crowed theater, surrounded by applause, and not be deafened? Do the bodies and seating absord the sound? Is the variation in the pitches of each clap a reason for no doubling of volume with each additional person? Or for that matter, how can we sit at a piano and bear the sound of five notes played at an equal volume--if all the notes were at the same pitch, would the sound be deafening?
NO! sound follows a Logorirhimic scale. i have a rough mentations of how this works but some others can xplaine it better . i think on pro rec sound there is a good article on this.

4. ## Re: Does the amplitude of a sound double when stacked?

Jake-

When two precisely identical waveforms (sounds) are stacked such that they are perfectly phase coherent ( precisely in phase), the sound waveform will indeed double (increase by 3db in power). Practically, this would be hard to do in dealing with re-recorded sounds, so that in general, it wouldn't happen. The sounds of an audience clapping would consist of a spectral forest of frequency and phase differences, and the power would only increase according to a root-mean-square (RMS) formulation.

Notice I refer to power increases, and not loudness increases. These are
somewhat different, but of course tend in the same direction. Loudness is governed by so-called Fletcher- Munson curves, and has frequency dependence. Remember the "loudness" control on stereo equipment which was side-by-side with a volume control?

But that's a little bit of a red herring here; the sounds of a large audience clapping will be somewhat like white noise, evenly distributed frequency wise, so that power=loudness.

So the answers are 1. Probably not, and 2. You won't get blown out of the auditorium because the loudness increases much more gently than a doubling every time another member starts clapping.

Carl

5. ## Re: Does the amplitude of a sound double when stacked?

The doubling of intensity applies only when the sound is in electronic form, be it analog or digital. It doesn't apply in acoustic environment as there are other conditions that affect the sound than just phase. There is intensity increase when constructive interference occurs, but the intensity doesn't exactly double.

The decibel scale is very logical, the human ear is less logical. We hear 10 times intensity increase as doubling sound level. The decibel scale is handy because with it a 3 dB increase sounds the same from 50 to 53 than 100 to 103, in both situations it is a barely audible difference. The human ear can detect intensities from 10^-12 W/m^2 to over 1 W / m^2. Isn't it simple to say that the human ear can detect intensity levels from 0 to 140 decibels?

The explanation to the applause question is complex. As was explained before, the acoustic environment and the difference between individual claps mean that there isn't much constructive interference between the claps. Other factor is the Haas effect. The human ear works in a way that when two identical or close to identical sounds (I assume that two handclaps can be close enough) arrive to the ear at similar level (the latter can even be slightly louder) within 40 milliseconds, the ear will only hear the first one.

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