Analysis

Analysis:

4/16/24:

Click for --> aerial photo

The following simple analysis shows how easy it would be for Target to provide ample safety for a driver who might be briefly on foot in the Target yard -- while not creating unlivable conditions for the adjacent neighborhood:

The greatest distance a Target yard-truck needs to back up is 35 feet. The nearest residential yard is 360 feet from the closest point for yard-truck backing.

According to theory -- which incorporates the area of a circle -- if a yard-truck's broadband white noise alarm reads 69 decibels at a distance of 35 feet, then it would read less than 50 decibels at 360 feet.

69 decibels is extremely loud and plainly stands out against the ambient background noise in the Target yard. (It would be perceived at minimally four times the background noise, and would have minimally 13 times the sound pressure as the background noise.)

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05/28/2024 note:

The "area of a circle" method is not nearly as accurate as considering the volume of a half-sphere:

My own measurements indicate that when the noise is of a broadband white noise type, a decibel reading of 80 at a distance of 37 feet will produce a decibel reading of about 50 at 360 feet. And 80 decibels is ear-damaging loud.
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50 decibels at the boundary of a residential yard is legal and acceptable by most people. Typical ambient background noise in a busy suburb is about 45 decibels.

And incidentally, Brigade's broadband white noise alarm operates at 82 decibels, measured at the source.

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Technical information:

Alarm device set such that a meter will read 69 decibels at a distance of 35 feet from the alarm. All other values follow from that, according to theory, using the area of a circle:

feet    decibels

   35      69 (see note four paragraphs down)
   45      68 (maximum)
   90      62 (maximum)
180      56 (maximum)
360      50 (maximum)

Using the "circle rule", when you double the distance, the sound pressure is reduced to 1/4 the amount. It is because the area of a circle is related to the radius by the square law; i.e., area = pi * radius ^2. The volume of a half-sphere is the more accurate method, though it also does not precisely correlate with emperical data.

A 3 decibel drop equates to 1/2 the sound pressure and therefore a 6 decibel drop equates to 1/4 the sound pressure, which equates to doubling one's distance from the source -- using the "circle rule".

The preceding relationships are what generates the values in the table above.

(Note: Again -- my own measurements indicate that a decibel reading of 80 at a distance of 37 feet will produce a decibel reading of about 50 at 360 feet, influenced by the volume of a half-sphere.)

Thus, 69 decibels equates to about 13 times the sound pressure as 50 decibels. i.e., a person 360 feet away would experience a sound pressure that is less than 1/13 the sound pressure experienced by the person who is 35 feet away from the source when the noise is of the broadband white noise variety.

That is according to the "circle rule". The actual effect, based on the "half-sphere", as well as on empirical data, is far more extreme (effective) -- with 80 decibels at 37 feet becoming merely 50 decibels at 360 feet.

A subjective and less accurate method for assessing sound difference is the 10 decibel rule, whereby a drop of 10 decibels implies a perceived drop in volume of 1/2. That would mean that going from 69 decibels to 50 decibels would be a four-fold drop in perceived sound. i.e., the person 360 feet away would sense a sound volume that is 1/4 the sound volume perceived by the person who is 35 feet away from the source.

It would be perceived as 1/8 the volume when going from 80 decibels to 50 decibels -- which is what is most relevant in this case, considering the "half-sphere rule", as well as the empirical data.