Sound intensity is related to pressure, and the unit of pressure is Pascal (abbreviated **Pa**). However, we don’t normally use Pa in describing sound intensity; we use the unit of **decibel (db)** instead. It is not necessary to understand all the mathematics involved in the conversion from Pa to db, but some basic understanding of the concept is useful. There are a few reasons why we use db in describing sound.

### Scaling

Human ears are very sensitive. We can hear a soft whisper as well as the sound of a jet engine, which is a billion (1,000,000,000,000) times more powerful than a soft whisper. Such a huge range can be best represented using a logarithmic scale, which the decibel scale is.

### Proportionality

More important than merely scaling down the unit of measurement, logarithm scale also corresponds well to how our ears respond to sound. In a quiet library, it is easy to be heard by simply whispering, but in a rock concert, the same whisper will not be heard at all. The reason is because in a rock concert, we need a proportionally louder sound in order for the ear to separate it from the music itself.

### Simple Arithmatics

Log scale converts multiplication to addition and division to subtraction. Say you want to proportionally increase the volume of your music by 25%. In the place where the volume is low (say 15 Pa), you will have to change the volume to 18.75 Pa (15 * 1.25), but in the place where the volume is high (say 350 Pa), you will have to change the volume to 437.5 Pa (350 * 1.25). We can see that for both numbers, it is a simple matter of multiplying the original number by 1.25, but we don’t come to those numbers easily without using a calculator.

If we use decibel scale, however, we only need to say that we increase the volume by 1.9 db, regardless of the original volume. Such a scaling is more intuitive for our brain to understand.

### Seeing Decibel Scale in Audacity

The default view of Audacity is a linear vertical scale with a normalized scale from -1.0 to +1.0. Below is an example of a stereo track shown in linear scale:

To switch to decibel scale, one can click on the track name (or the black triangle) in the Track Control Panel (shown in the the red ellipse in the picture below). A drop-down menu will appear. Choose “Waveform (db).”

And below is the same audio in decibel (logarithmic scale):

For our practical purposes, it is good to know that increasing sound level by 6 db will double its volume, and decreasing by 6 db will half its volume. This is an approximation as perception by each individual is different.

And that is all we need to know about decibel scale in order to use it. Any other detail will be described when we talk about specific effects.

I realize that there is a lot of simplification in the mathematics of decibel scale (and you probably will never need the details anyway), but if you have any question about decibel scale, please feel free to leave a question in the comment area.

Now we are ready to move on to some Audacity effects and examine some parameters in details.

In acoustics, and several other fields, decibels (dB) are used to denote magnitudes. In the case of acoustics sound pressure level (stated in decibels) is much more convenient than the stating of the actual sound pressure in Pascals.

1. In the range of human hearing, roughly 0 dB to 120 dB, indicate the numerical values if that same range where to be stated in terms of sound pressure with Pascals as the units. Discuss this as a rationale to denoting magnitudes in terms of decibels.

2. When determining the combined sound pressure level of two separate sound sources, how is that numerical summation accomplished?

3. Discuss how the magnitude of the perceived sound pressure level from a stationary noise source changes as the person moves away from the sound source and how a person’s perception of that sound (half as noisy, twice as noisy, etc.) is related to the change in decibel levels