# Sound Pressure Level Formula

Sound pressure is the pressure applied by the sound waves. Sound pressure level is the is the ratio of the actual sound pressure and the reference level which is the lowest intensity sound that can be heard by maximum people. In other words, sound pressure level decides the amount of pressure on the sound.  It provides the logarithmic measures of rms value of the sound pressure to the reference value of the sound.

It is expressed in (dB).

The sound pressure level formula is expressed by,

Lp = 20 log10 (prms / pref)

Where,

p = root mean square sound pressure in Pa,

po = reference sound pressure in Pa. (20 μPa)

Example 1: Calculate the rms pressure level if the sound pressure level is 40 dB?

Solution:

Given:

Sound pressure level = 40 dB,

pref = 20 μPa.

The sound pressure level formula is given as,

Lp = 20 log10 (prms / pref)

The pressure level is given by,

e(Lp / 20) = (prms / pref)

e(40 / 20) = prms / (20×10−6)

4.85 × 108  = prms / (20×10−6)

Therefore, prms = 9.703 × 103 Pa.

Example 2: Determine the sound pressure level if the rms pressure value is given as 30 μPa.

Solution:

Given:

Prms = 30 μPa,

pref = 20 μPa.

The sound pressure level formula is given by,

Lp = 20 log10 (prms / pref)

= 20 log10 (30 / 20)

Therefore, Lp = 3.52 dB