How Does Sound Spread — What Effect Does Distance Have on Decibel (dB) Levels?

Hi. I'm not a physics expert; I had only very basic acoustic physics high school.

You can find brochures everywhere on the internet that show what decibel (dB) level is harmful to a human ear, or more precisely, how long can a human ear withstand a particular dB level before it can be damaged from noise exposure.

However, there is no explanation how far can a person safely be from some source emitting a noise at particular volume. I don't know if you understand what I mean.

Imagine a device emitting a sound at X dB. A person would be standing Y meters away from the device. How many dB would the noise be the person hears? Is it possible to calculate that with some equation? I know that dB is a logarithmic unit so it isn't trivial.

Also, it looks like high frequencies can't penetrate through environment as much as low frequencies because if someone is far away from a disco, they hear only bass. So I suppose the pitch of the sound is another factor in the equation.

 

For every 2x of distance, the sound level reduces by 6 dB (e.g. moving from 10 to 20 metres away from a sound source). But the next 6 dB reduction means moving from 20 to 40 metres, then from 40 to 80 metres for a further 6 dB reduction.

How Sound Reduces With Distance From a Point Source

 

There is a whole science behind this (acoustics), but I'll try and give a few brief answers here...

Not all frequencies dissipate at a similar rate across distance. There are "waterfall plots" that illustrate this. A blast of pink noise is played through a specific speaker (monitor in audio terms) and the resultant emittance can be measured and plotted. The same pink noise burst will have different characteristics based on what monitor plays it back. Here is an example chart, you can see the lower frequencies travel longer before dying out (hence your "bass outside of a club" example)



Another thing to consider is that low frequencies can be called omnidirectional for all practical purposes, where as higher frequency sounds are very directional in the presentation. You may have had the experience of being near an electrical device emitting a high frequency buzz and found that there is a narrow "sweet spot" that you need to have your head in in order to hear it, whereas when a large truck drives by, the rumble just sounds (and feels) like it's coming from all around you.