The faintest sound heard by a human ear = 0.000,000,000,000,000,1 watts = 10^-16 watts. The loudest, tolerable sound heard by a human ear = 0.000,1 watts = 10^-4 watts. This is a range of 10,000,000,000 = 10^10. If we were to plot these two points on a graph, the two points would simply be too far apart for analytical purposes (not to mention they would not fit on the same piece of paper). A logarithmic scale allows us to analyze this large data range for sound.

Most noise sources are measured in terms of intensity, or strength of the sound field. The standard unit, one-decibel (db), is the amount of sound that is just audible to the average human. The decibel scale is made logarithmic; each unit is 10 times the preceding one. The decibel scale is somewhat misleading because it is logarithmic rather than linear; for example, a noise source measuring 70 dBA is twice as loud as a source measuring 60 dBA and four times as loud as a source reading 50 dBA. A barely audible whisper measures 10 decibels and a speeding express train about 100 decibels, though the train generates 10 billion times as much sound energy. This misleading difference can also be seen in Earthquakes using the Richter Scale, which is a logarithmic scale like sound. A magnitude of 5.3 on the Richter scale is a moderate earthquake, and a strong earthquake has a magnitude of 6.3. Thus like sound, a small difference in value actually means a great difference in intensity.

To illustrate the "real" differences in sound intensities, please refer to the below table for values and a sample calculation. Using the decibel formula, we can find the intensity difference between two sound levels. Using 80 decibels as a reference, the intensity difference between all the aircraft has been plotted below. As illustrated, the Intensity difference is almost 5,000 times for a F/A-18 taking off. The values for the other aircraft cannot been seen on the chart since the differences are so great between the F/A 18 and the commercial aircraft (hence the reason for logarithmic scale). Of course a F/A 18 taking off is not 5,000 times louder to human ears than 80 decibels, but 5,000 times the sound energy. To determine the perceived loudness, a different unit of measurement is needed called the Sones. Using the following general formula of doubling the number of Sones for each 10-decibel increase, a F/A 18 departing is sixteen times as loud.

Sample calculation:

D db =10 log 10 (I f / I i) where D db is the change in decibels and (I f / I i) represents the Intensity.

Calculate the Intensity between a Boeing 737 departure and a F/A-18 departure.

Boeing 737 at departure =80.8 dB

F/A-18 at departure 117 db

D db = 117-80.8 = 36.2

36.2= 10 log 10 (I f / Ii)

3.62= log 10 (I f / I i)

I f / I i=10 3.62

I f / I i= 4,168 which means that I f (F/A-18 Intensity) = 4,168 times I i (Boeing 737 Intensity)