contestada

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?

Respuesta :

Answer:

Given that

β= 120 dB at 5 m

We know that sound intensity given as

[tex]\beta =10dB\log\dfrac{I}{I_o}[/tex]

[tex]120 =10\log\dfrac{I}{10^{-12}}[/tex]

I= 1 W/m²

Power producing by loud speaker

P = I  x 4πr²

[tex]P=1\times 4\pi \times 5^2\ W[/tex]

P=314.15 W

a)

Let take intensity at 35 m is I'

r'=35 m

I'=P/4πr'²

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

I'=0.0204 W/m²

b)

Given that

β'= 80 dB

[tex]\beta' =10dB\log\dfrac{I'}{I_o}[/tex]

[tex]80=10\log\dfrac{I'}{10^{-12}}[/tex]

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

Otras preguntas