Question

At a distance of 8 m, the sound intensity of one speaker is 66 dB. If we were to place 3 speakers in a circle of radius 8 m, what woud the sound intensity level be at the center of the circle

Answer 1

dβ = 70. 77 dβ

Step-by-step explanation:

The intensity of sound in decibels is

dβ = 10 log I/I₀

let's look for the intensity of this signal

I / I₀ = 10 dβ/10

I / I₀ = 3.981 10⁶

the threshold intensity of sound for humans is I₀ = 1 10⁻¹² W / m²

I = 3.981 10 ⁶ 1 10⁻¹²

I = 3,981 10⁻⁶ W / m²

It is indicated that 3 cornets are placed in the circle, for which total intensity is

I_total - 3 I

I_total = 3 3,981 10⁻⁶

I_total = 11,943 10⁻⁶ W / m²

let's reduce to decibels

dβ = 10 log (11,943 10⁻⁶/1 10⁻¹²)

dβ = 10 7.077

dβ = 70. 77 dβ