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Question

Sound with intensity larger than 120dBappears painful to a person. A small speaker delivers 2·0W of audio output. How close can the person get to the speaker without hurting his ears?


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Solution

Step 1: Given data:

The level of the sound is =120dB

The audio output = 2·0W

Step 2: Formula used:

It is understood that,

Soundintensitylevel(IL)=10logII

Where, I is sound intensity

Io is reference intensity

Intensity(I)=power(P)Area(A)

Step 3: Compute the intensity of sound:

On putting the given values in the formula of sound intensity level-

120=10·log10II1012=II

Since, I=10-12wm2. So,

The value of sound intensity will be-

I=1wm2

Step 4: Compute the closest distance:

We know that,

Intensity=powerArea

Suppose the nearest distance is x.

The area will be- A=4πx2

So, using the formula we get-

I=P4πx21=24πx2x2=12πx=0.4m

Thus, the nearest distance that a person can go is 0·4m.


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