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?

83dB

Explanation:

first we must convert decibels to intensity in

decibels:

we use the following equation for the conversion:

Where is the intensity corresponding to the 86 decibels, and It is the minimum intensity that the human ear perceives:  

So replacing , and clearing for

Now we use the exponential of 10 because this will cancel the logarithm.

Since , we have:

And because instead of two firecrackers now is only one, the intensity is reduced by half:

And now returning to the decibel unit:

we want to find the decibel value corresponding to the new intensity

≈ 83dB

the sound level if only one is exploted is 83dB

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