Comparison of Sound Intensity Level (SL)
Sound Pressure Level (SPL)
SL = 10 x log (I/) where I is the intensity in watts/m. The unit is decibel, denoted "dB". For the hearing threshold, I/ = 1 and SL = 0 dB. For the feeling threshold, I/ = 10 = 120 dB.
Note that when a quantity is expressed in decibels a relative measure is given. That is, it is given with respect to some reference value ( in the case of SL). Whenever the intensity (I) is multiplied by a factor of 10, one just adds ten decibels to the value of SL. Whenever the intensity is multiplied by a factor of 100, one just adds 20 decibels to the value of SL.
Now, there is a relation between the intensity of a sine sound wave (I) and the value of the average pressure variation Dp. (Dp= pressure variation amplitude divided by 2.)
where V is the velocity of sound in air and is the air density. For normal conditions of air and temperature,
I = 0.00234 x Dp. Dp is in Newton/m .
Now the threshold of hearing is 10 watt/m. According to this expression for I above, this represents an average pressure variation of only 2.0 x 10Newton/m.
This relation also shows that I is proportional to the square of Dp, thus
Thus the quantity Sound Pressure Level (SPL):
SPL = 20 log .
For a travelling wave, the numerical values of SL and SPL are identical and SPL and SL are one and the same thing.
Now, for standing waves, there is no energy flow at all and the intensity I cannot be defined, hence SL loses its meaning. Yet the concept of average pressure variation Dp at a given point in space (at the entrance to the auditory canal for example) remains meaningful. That is why SPL is more frequently used than SL.
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