Question

An outside loudspeaker (considered a small source) emits sound waves with a power output of 102 W.

(a) Find the intensity 11.5 m from the source.
W/m²

(b) Find the intensity level in decibels at that distance.
dB

(c) At what distance would you experience the sound at the threshold of pain, 120 dB?
m

Answer 1

a)

The formula for intensity is given by:

Here P = 102 W and R = 11.2 m

Putting these values we obtain:

b)

The intensity level in decibels  is given by:

where I₀ = 10^-12

Putting these values we obtain:

c)

Given that:

The corresponding I = 1 W/m²

Thus putting I and P in the first equation relation for R we get: