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Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

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BuyFindarrow_forward

Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

You are working at an open-air amphitheater, where rock concerts occur regularly. The venue has powerful loudspeakers mounted on 10.6-m-tall columns at various locations surrounding the audience. The loudspeakers emit sound uniformly in all directions. There are ladder steps sticking out from the columns, to help workers service the loudspeakers. Many times, audience members break through the protective fencing around the columns and climb upward on the columns to get a better view of the performers. The upcoming concert is by a group that states that several very-high-volume pulses of sound occur in their concerts, and these sounds are part of their artistic expression. The amphitheater owners are worried about people climbing the columns and being too close to the loudspeakers when these peak sounds are emitted. They do not want to be held responsible for injuries to audience members’ ears. Based on past performances of the group, you determine that the peak sound level is 150 dB measured 20.0 cm from the speakers on the columns. The owners ask you to determine the heights on the columns at which to mount impassable barricades to keep people from getting too close to the speakers and hearing sound above the threshold of pain.

To determine

The height on the column at which to mount the barricades to keep people safe.

Explanation

The height of the speakers column is 10.6m and the intensity level heard at 20cm away from the speaker is 150dB.

The humane ear threshold intensity is 1.00W/m2.

The threshold intensity constant is 1012W/m2.

The formula to calculate the intensity of a sound is,

    I=I010β10

Here, I0 is the threshold intensity and β is the intensity level.

Substitute 150dB for β and 1012W/m2 for I0 in the above equation.

    I=(1012W/m2)10150dB10=100W/m2

The formula to calculate the power of the sound is,

    P=I4πr2

Here, r is the distance from the source.

Rearrange the above equation for r,

    r=I4πP        (1)

The minimum distance at which the speaker produces the intensity of human ear threshold is,

    r=Ith4πP        (2)

Here, Ith is the human ear threshold intensity.

Divide equation (1) and (2).

    rr=I4πPIth4πP=IIth

Substitute 100W/m2 for I, 1

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