Question

A rock band playing an outdoor concert produces sound at 120 dB 5.0 m away from their single working loudspeaker. Ignore sound reflected from walls and other objects and consider sound originating directly from the speakers.

a. What is the sound intensity level 35 m from the speaker?
b. How far away from the speaker should you stand to ensure the intensity does not exceed 80 dB?

Answer 1

Given that

β= 120 dB at 5 m

We know that sound intensity given as

`\beta =10dB\log(I)/(I_o)`

`120 =10\log(I)/(10^(-12))`

I= 1 W/m²

Power producing by loud speaker

P = I x 4πr²

`P=1* 4\pi * 5^2\ W`

P=314.15 W

a)

Let take intensity at 35 m is I'

r'=35 m

I'=P/4πr'²

`I'=(314.15)/(4\pi * 35^2)\ W/m^2`

I'=0.0204 W/m²

b)

Given that

β'= 80 dB

`\beta' =10dB\log(I')/(I_o)`

`80=10\log(I')/(10^(-12))`

I'=10⁻⁴ W/m²

Let's take at distance r intensity is 80 dB

P=314.15 W

P = I' x 4πr'²

314.15 = 10⁻⁴ x 4πr'²

r'=500.11 m