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

Answer

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

$\beta = 10 log(\dfrac{I}{I_0})$

I₀ = 10⁻¹² W/m²

now inserting the given values

$101= 10 log(\dfrac{I}{10^{-12}})$

$10.1= log(\dfrac{I}{10^{-12}})$

$\dfrac{I}{10^{-12}}= 10^{10.1}$

$I =10^{10.1} \times 10^{-12}$

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