Question

If two firecrackers produce a sound level of 86 db when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [hint: add intensities, not db's.]

Answer 1

By definition, sound intensity, I, in terms of decibels is

`I_(db) =10 \,log( (I)/(I_(0)) )`
where
I₀ = reference intensity.

With two sound sources,

`10 \, log( (2I)/(I_(0)) ) = 86 \\ log( (2I)/(I_(0)) ) = 8.6 \\ (2I)/(I_(0)) =e^(8.6) \\ (I)/(I_(0)) =e^(8.6)/2 = 2715.83`

Therefore with one sound source, the decibel level is

`10 \, log( (I)/(I_(0)) ) = 10 \, log(2715.83) = 34.34 \, db`

Answer: 34.3 db