The reason for using decibels is to compress the immense range of watts we can hear, 0.000000000001 watts up to 100 watts or more, into manageable numbers. Similarly the range of sound pressure levels we can hear is 0.00002 Pascals up to 200 Pascals. Converting these levels into dBs results in a range of values 0 dB up 140 dB, much easier to 'handle'.
However sound level calculations involve logarithms which many people are not comfortable with, so we describe a simpler modern way.
First the basics
Sound Power Level (Lw) = 10·log (w/wo) dB, where w is the sound power in watts and wo is the reference sound power level of 10-12 watts ≡ 0 dB **
3 dB = a factor of 2 in sound energy (+3dB is double the sound power and 3dB less is half the power)To see a table of typical sound power levels and other 'rules of thumb', click here
** When you divide watts by the reference watts, for example, the result is a simple ratio (no units).
Sound Pressure Level (SPL) = 20·log (p/po) dB, where p is the sound pressure in pascals and po is the reference sound pressure of 0.00002 pascals ≡ 0 dB in air = the threshold of hearing at 1KHz
6 dB = a factor of 2 in sound pressure i.e. doubling or halving the sound pressureTo see a table of typical sound pressure levels and 'rules of thumb' click here
To understand the 10·log sound power vs the 20·log sound pressure formulae see our root power quantity entry. See also the IEC decibel definition
Sound Level Calculations
Acoustic engineers often use Excel spreadsheets to add, subtract and average acoustic levels like the following tables. If you don't have access to this software or the experience to programme spreadsheet columns you can simply use the Bing or Google search box, as follows
|10·log(w/wo)||w/wo||w/wo totals||10·log (w/wo) totals|
|60 dB||1,000,000||2,000,000||63.01 dB|
|70 dB||10,000,000||12,000,000||70.79 dB|
|61 dB||1,258,925||13,258,925||71.23 dB|
Column 1 lists the dB levels we want to add up, note the column headings
In column 2 we remove the 10·log conversion by simply typing 10^(60/10) into Bing or Google to convert the 60 dB levels back to sound power ratios and the correct, precise answer is 1,000,000
Then enter 10^(70/10) into the search engine to convert the 70dB and finally 10^(61/10) to convert the 61dB level
Column 3 is the arithmetic running total of the w/wo (sound power quantities).
In Column 4 we have re-converted the running totals back to decibels using Bing or Google again, this time entering 10*log (2,000,000) for row 2, the addition of (60 dB + 60 dB). Next enter 10*log (12,000,000) into the search engine for the row 3 total and finally log 10*log(13,258,925) = 71.23 dB and is the sum of the four dB levels
The above example also confirms the 'rule of thumb' that 3 dB is a factor of 2 and 10 dB = a factor of 10 when dealing with sound energy levels.
Incidentally Google also says the average sound power level is 10*log (13,258,925/4) = 65.20 dB
|20·log(p/po)||p/po||p/po totals||20·log (p/po) totals|
|60 dB||1,000||2,000||66.02 dB|
|70 dB||3,162||5,162||74.26 dB|
|61 dB||1,122||6,284||75.96 dB|
Sound pressure level calculations are the same as sound power level calculations detailed above, except for the 20 log factor, instead of the 10 log power factor, which results in the 6 dB 'rule of thumb' concerning doubling or halving sound pressure quantities, not the 3 dB 'rule' that applies to sound power levels.
The average sound pressure level = 20*log (6,284/4) = 63.92 dB
** The above calculations do not hold true if the original dB measurements were not consistent, i.e. similar situation, identical measurement periods and the same frequency or time weightings if used.