Guitar resonance and soundhole geometry – Part 11: THE ACOUSTIC UNITS USED IN THE EXPERIMENT AND WHY

PART 11: ACOUSTIC UNITS

Most people are familiar with the unit decibel (dB), which is commonly used to describe environmental sound levels.

The dB scale ranges from 0 (the softest sound that most human ears can pick up) to 130dB (the sound level so loud the it causes pain rather than the accurate perception of a sound).

Everyday examples of dB levels are: 30-40dB in a library; 70-80dB traffic on a busy road; 110-120dB pneumatic drill. For correct use in acoustics, the application of the scale is complex because it has to take into account the fact that the human ear responds differently to different frequencies, as well of other technical factors. This corrected scale is called the dB(A) scale.

However, the important thing to know about the dB unit is that the scale is not linear, but logarithmic. What this means is that a sound at 100dB pushes energy into your ear at not twice the rate of a 50dB source, but 100,000 times (x105). 

You might think that 100dB would be twice as loud as 50dB, but in fact a sound twice as loud as 50dB measures at about 53dB.

This isn’t done to be difficult. It’s because the range of human hearing is so great that a linear scale just can’t easily encompass the numbers when expressed as the rate at which energy hitting your ear.

Without going into any more details, here are some examples to think through:

  • plus 3dB means approximately a doubling of the sound intensity
  • 60dB is ten times the intensity of 50dB
  • 70dB is one hundred times more intense than 50dB
  • 30dB is one hundredth of the intensity of 50dB
  • 47dB is half the intensity of 50dB

One effect of this is that you can’t add or subtract dB as if they’re familiar numbers (50dB plus 50dB is roughly 53dB). For this and other reasons you’ll see that I express my results in power terms – that is the amount of energy falling onto the eardrum every second. The unit is Watts/square metre (W/m2), and the symbol is I.

I also do this because during my analysis of raw data I subtract closed box response from the signal I get from the microphone, and I need to use a non-logarithmic scale.

To give you and idea of how this works, here are some examples of dB readings converted to Intensity:

  • 0dB is I0or 1 x 10-12 W/m2(0.000000000001 W/m2)
  • 3dB is about 2 x 10-12W/m2
  • 10dB is 1 x 10-11W/m2
  • 50dB is 1 x 10-7W/m2
  • 100dB is 1 x 10-2W/m2

Here is a more complete set of conversions:

β (dB)I (W/m2)
01.000E-12
101.000E-11
201.000E-10
301.000E-09
401.000E-08
501.000E-07
601.000E-06
701.000E-05
801.000E-04
901.000E-03
1001.000E-02
1101.000E-01
1201.000E+00

I also think that unless you are really familiar with how the dB scale works, looking at measurement results that use them can be quite misleading – what looks like a small dip of 3dB actually represents a halving of the sound intensity, for example.

This discussion isn’t central to understanding my results, but as a reader you might be expecting to see the dB scale being used.

There is one final complication that you need to be aware of. I am very careful to present my data and conclusions in terms of RELATIVEresponse. I have only measured how the various aircavity/soundhole combinations respond relative to the response of no soundhole at all – a closed box. 

You can only use my numbers to compare, not to predict the actual response of a real guitar soundhole.

In addition, Audacityrecords sound levels on a minus scale. Most digital recording apps do the same, because in recording quality sound such as music it is important to avoid clipping – distortion introduced by a signal that is too intense for the software to handle. Using 0dB on a recording as the maximum level possible helps to identify and control clipping.

It also complicates dealing with data in my experiments. Because I must work in Intensity (W/m2), you can probably see that in the real world 0dB is the lowest sound a human can detect, and anything in the subzero range is rather meaningless.

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