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

Answer:

Given that

β= 120 dB at 5 m

We know that sound intensity given as

$\beta =10dB\log\dfrac{I}{I_o}$

$120 =10\log\dfrac{I}{10^{-12}}$

I= 1 W/m²

Power producing by loud speaker

P = I  x 4πr²

$P=1\times 4\pi \times 5^2\ W$

P=314.15 W

a)

Let take intensity at 35 m is I'

r'=35 m

I'=P/4πr'²

$I'=\dfrac{314.15}{4\pi \times 35^2}\ W/m^2$

I'=0.0204 W/m²

b)

Given that

β'= 80 dB

$\beta' =10dB\log\dfrac{I'}{I_o}$

$80=10\log\dfrac{I'}{10^{-12}}$

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