Remember: SPL2 = SPL1 minus 20 times the log of (R1 over R2)
where R is the distance in metres from the source of the sound and SPL is the sound level in decibels at that distance.
We know that at 1 metre away (R1) the sound level is 100 decibels (SPL1). Use the formula above to solve for the sound level at the first aid tent (SPL2), if the tent is placed 75 metres from the speaker (R2).
How loud will it be at the first aid tent?
First, let’s fill in the values that we know:
SPL2 = 100 minus 20 times the log of (75 over 1)
We can simplify this as follows:
SPL2 = 100 minus 20 times the log of (75)
SPL2 = 100 minus 20 times 1.875
SPL2 = 100 minus 37.5
SPL2 = 62.5 decibels
The sound level in the first aid tent is 62.5 decibels.