Arock band playing an outdoor concert produces sound at 120db 5.0m away from their single working loudspeaker. a.)what is the intensity (i) 5 m from the loudspeaker? b.) what is the power produced by the loud speaker? c.) what is the intensity (i) 35 m from the speaker? d.) what is the sound intensity level 35m from the speaker?

a) 1 W/m^2

The sound intensity level () is defined as

where

I is the intensity of the sound

is the reference sound intensity

dB is the decibel

For the sound wave in the problem we have

So we can solve the formula to find I, the sound intensity:

b) 314 W

The intensity is related to the power by

where

P is the power

r is the radius of the area considered (so, the distance from the source)

In this case, we have

r = 5 m

So the power of the sound is

c) 0.02 W/m^2

The sound intensity follows an inverse square law:

where we have

is the sound intensity at r = 5 m from the source

is the sound intensity at r = 35 m from the source

Solving the equation for I2, we find

d) 100.3 dB

The sound intensity level is given by

where in this case we have

Substituting this value into the equation, we find

wavelegth as in spectrum red oygbiv

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