Sound Pressure Over Distances (Technical post) – Mervyn Augustine
One of our firm’s favorite part of the job is system design. In today’s blog post, and continuing from last week’s post on Loudspeaker Specifications NOT to ignore, we get very technical in looking at how the sensitivity of loudspeakers affects our choice in speaker during the design.
This is by no means a comprehensive, be-all-end-all condition – there are multitudes of factors to consider beyond this. However, this post is a glimpse of one of the technicalities that goes through our designer’s minds when approaching system design.
Sound Pressure (SP) is the deviation between ‘local pressure’ and ‘ambient pressure’, the SI unit for SP is Pascal (Pa), while the more commonly known Sound Pressure Level is measured in decibels (dB).
Sound Pressure Level is measured by a calibrated microphone.
Let’s get right into it :
The sound pressure p = F / A is given as N/m2 = Pascal (Pa).
The sound pressure p (pressure ) is force F (force) through area A (area). p ~ 1 / r
The change of the sound pressure is following the “1 / r law”, the distance law. For example, the sound pressure p is decreased to half the value, if the distance is doubled from the sound source.
The double distance 2 × r changes the sound pressure level compared to 1 × r:
Change in Lp =20×log1/2=20×log0.5=(–)6dB
Distance law for sound pressure:
p2 /p1 = r1 /r2
Sound pressure waves propagate linearly, when their sound pressure is halved at double the distance. The decrease of the sound pressure follows the “1 / r law” (Distance law).
In relation to the sensitivity of speakers, for example, a 90dB
(1M, 2.83V) rated speaker, would measure at 84dB at two meters, and 78dB at four meters.
Coinciding with the amount of power required to achieve 90dB at four meters, note that every 3dB increase requires double the power, and that takes 1 watt to 16 watts, from 1 meter to 4 meters.
There are certainly more things to consider, i.e.: the total amount of speakers used, be-it in stereo, or multi-channel audio, if the impedance is equal throughout the frequency response, but this provides a very good guideline, when considering how much power is required with your choice of speakers.
’til next week, thanks for reading.