Sound attenuation (generator application)

[mshields]

I received noise attenuation information pertaining to an outdoor generator enclosure which indicated a 30dB reduction at 3 feet. I thought it was typical to give these values at 23 feet and asked about this. Here is the response I got:

We can change that to 23 feet if you want.
It really does not matter.
If the unit is 100 db/a at 3 feet (no housing) that means it is est @ 91 db/a at 23 feet.
So 30 db/a reduction at 3 feet = 70 db/a
So 30 db/a reduction at 23 feet = 61 db/a


I'm wondering if given the non-linear nature in which noise drops off with distance, I'm wondering if this is true?

Thanks,

Mike

 

[gar]

080808-2158 EST

mshields:

Assume the generator is an isotropic radiator, radiates equally in all directions. The power density will vary as the inverse of the square of the radial distance.

In your example the ratio of radii is 3 to 23 a ratio of 7.67. Square this and the result is 58.8. Thus, the power density at 23 ft is 1/59 of that at 3 ft. Using this ratio I get a greater DB change than you indicated, and thus it is probably an empirically determined attenuation, and not a perfect isotropic radiator and that is to be expected.

.

 

[broadgage]

The decibel is not a linear unit, like say a watt, it is a ratio of one noise or signal level to another.

For example 100 watts is twice the power of 50 watts, but 100 decibels is not twice the power of 50 db, it is a great deal more than twice the power.

 

[Smart $]

...
I'm wondering if given the non-linear nature in which noise drops off with distance, I'm wondering if this is true?

Actually, drop off rate depends on the "field" where measurements are taken.

If taken in the free field (open space with no reverberant obstacles), the inverse square law for sound intensity becomes the inverse distance law for sound pressure.

Rather than explain this, please refer to the Master Handbook of Acoustics, Chapter 4: Sound Waves in the Free Field.

Ultimately though, yes a 30 dba reduction at 3 feet will effect a 30 dba reduction at 23 feet.

 

[mdshunk]

61 or 58.8? Po-tay-toe, pa-tah-toe.

 

[Smart $]

080808-2158 EST

mshields:

Assume the generator is an isotropic radiator, radiates equally in all directions. The power density will vary as the inverse of the square of the radial distance.

In your example the ratio of radii is 3 to 23 a ratio of 7.67. Square this and the result is 58.8. Thus, the power density at 23 ft is 1/59 of that at 3 ft. Using this ratio I get a greater DB change than you indicated, and thus it is probably an empirically determined attenuation, and not a perfect isotropic radiator and that is to be expected.

.

The info provider used the wrong formula (inverse square, intensity):

100 dba + 10 log(3/23) = 91 dba​

The correct calculation is (inverse distance, pressure):

100 dba + 20 log(3/23) = 82 dba​

Therefore:

100 dba ? 30 dba = 70 dba@3ft
70 dba + 20 log(3/23) = 52 dba@23ft​