Question

A speaker at an open-air concert emits 500 W of sound power, radiated equally in all directions.

Part A:

What is the intensity of the sound 6.8 m from of the speaker?

Express your answer to two significant figures and include the appropriate units.

Part B:

What sound intensity level would you experience there if you did not have any protection for your ears?

Express your answer using two significant figures. Units must be in (dB)

Part C:

Earplugs you can buy in the drugstore have a noise reduction rating of 23 decibels. If you are wearing those earplugs but your friend Phil is not, how far from the speaker should Phil stand to experience the same loudness as you?

Express your answer to two significant figures and include the appropriate units.

Answer 1

A)

Intensity at a point is defined as,

.........................equation (1)

since the power is distributed equally in all radial directions, the "area is just the area of the sphere of radius of the given distance."

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b)

The intensily level in "decibals" is defined as

in dB

where

Hence putting the value of intensity in this equation as we got in the above problem is

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c)

The decibel required for Phil is 23 dB less than received by me.

Hence Phil will receive (119.35-23 )dB= 96.35 dB

Intensity received by Phil :

the distance at which Phil is standing :

from this equation rearranging, we get

putting this in equation (1) , of the problem (a)