Transcript: Calculate sound level over distance fill in the blanks

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.

Question

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?

Hint

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

Answer

The sound level in the first aid tent is 62.5 decibels.