You are on the design team for a new airport. The developer wants to build a hot

Question

You are on the design team for a new airport. The developer wants to build a hotel as close to the airport as possible. The intensity level of a large jet during takeoff is 140 dB at 50 m from the jet. The developer wants to build the hotel such that the intensity level heard by guests is not higher than 41 dB inside the hotel rooms and not higher than 122 dB in the parking lot of the hotel.

Part A

How far from the airport would you suggest the developer build the hotel?

Express your answer with the appropriate units.

122.5m

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Part B

What is the maximum allowable intensity I of the sound in the hotel rooms?

Express your answer with the appropriate units.

6.034•1011Wm2

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122.5m

Explanation / Answer

intenisty level B = 10 dB log(I/Io)

also I is intensity = power /area = P/4pi r^2

so I is inversy prop to 1/r^2

so

B2-B1 = 10 dB log(r1^2/r2^2)

140 - 41 = 10 dB log (r1^2/r2^2)

log(r1^2/r2^2) = 99/10 = 9.9

r1^2/r2^2 = 10^9.9 = 7.94 e 9

r2^2 = 7.94 e 9/(50*50)

r2 = 1.782 km

------------------------------------------------------------------------

use 140 = 10 dB * log(I/Io)

log*(I/Io) = 14

I/io = 10^14

I = 1e 14 * 1e -12 = 100 W/m^2

now use

I2/I1 = r1^2/r2^2

I2 = 100 * 50*50/(1782 * 1782)

I2 = 0.0787 W/m^2

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