**Comparison of Sound Intensity Level (SL)**

**and**

**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.