How do you measure a sound wave loudness?
Thanks in advance.
A sound level meter that measures sound pressure levels is the most common.
In dB I think.
You would think so wouldn't you, but not quite. Loudness is usually quoted with a frequency since the ear does not perceive all frequencies equally. The phon and the sone are common units of loudness, although I believe the sone is the standard unit, but I could be wrong.
Most conventional studies are indeed done in dB. However, the ear's interpretation of sound requires the altering/filtering of the source measurements. Hense the A, B, C and D weightings. The A weighting being the filter used most commonly and thus why most readings being quoted in dBA. Sones are used, but I think the dB rules supreme in this area.
Normally sound intensity is measured in dB relative to the minimum perceivable sound intensity of the human ear measured in units of W/m^2 (which turns out to be 1x10^-12 or something of that order).
So a sound level of 20 dB means that the sound intensity is 100x the minimum aubible level. 30 dB means the sound intensity is 1,000x, 40 dB 10,000x and so on.
As has been pointed out, this is not the only way to measure sound 'loudness', but this is the most common way it is measured in my experience as a layperson.
This is not exactly what I ment.
It is true that the human ear percieve sound loudness relative to its frequency and relative to the average sound in the environment.
However, I want to know the mathematical side of sound loudness.
Lets say we have two different sound waves that have a very close frequency.
What mathematical operation we need to do on the two sounds to tell which one is louder? Is it an integral on the absolute value of the wave amplitude?
Is it some other norm?
For example, if we have two sound waves that have the same frequency, one is a square wave and the other is a sin wave, who will be louder?
A square sound wave? That would imply an almost infinite acceleration of the sound producing device/thing. The forces generated would be huge. I don't think it's practical to look at it like that.
Since the interpretation of loudness is highly subjective, I would say that two things would be required. The first is a thorough understanding of the pressure field created by the source. The second is to understand the filtering characteristics of any of the weighting schemes.
It's just a function of the amplitude:
Since our hearing is basically logarithmic (similar to most of our senses, which allows a large range of input), the decibel scale is the same.
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