Question

An audio engineer takes decibel readings at distances of r1 = 13 m and r2 = 24 m from a concert stage speaker during a sound check. When he is r1 from the speaker, the engineer registers a decibel level of β1 = 101 dB on his loudness meter.

Answer 1

given,

Distance for decibel reading

r₁ = 13 m

r₂ = 24 m

When the engineer is at r₁ reading is β₁ = 101 dB

now, Calculating the Intensity at r₁

Using formula

`\beta = 10 log((I)/(I_0))`

I₀ = 10⁻¹² W/m²

now inserting the given values

`101= 10 log((I)/(10^(-12)))`

`10.1= log((I)/(10^(-12)))`

`(I)/(10^(-12))= 10^(10.1)`

`I =10^(10.1) * 10^(-12)`

I = 0.01258 W/m²

now, calculating power at r₁

P₁ = I₁ A₁

P₁ = 0.01258 x 4 π r²

P₁ = 0.01258 x 4 π x 13²

P₁ = 26.72 W