You are on the design team for a new airport The developer w

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 49 dB inside the hotel rooms and not higher than 118 dB in the parking lot of the hotel.

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

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

Solution

Let us first find intensity at 140dB, 118dB and 49dB

Use equation,

= 10dBlog(I/I₀)

140dB= 10dBlog(I/10^-12)   => I₁₄₀ = 10^2 W/m^2

118dB= 10dBlog(I/10^-12)   => I₁₁₈ = 10^11.8*10^-12 = 10^-0.2 W/m^2

49dB= 10dBlog(I/10^-12)   => I₄₉ =10^4.9*10^-12 =  10^-7.1 W/m^2

Part A)

We know I \' / I = ( r/ r \') 2

           10 -^0.2 / 10 ² = ( 50 / r \' ) ²

               10 ^-2.2 = ( 50 / r \' ) ²

   r \' = 629.46 m

  Developer should build the hotel beyond 629.46 m

Part B)

Intensity level at a distance r \' is L \' = 49 dB

We know L \' = 10 log ₁₀ ( I \'/Io)

          49 = 10 log ₁₀ ( I \'/Io)

log ₁₀ ( I \'/Io) = 4.9

   ( I \' /Io) =10 ^4.9

              I \' = Io 10 ^4.9

              = 10 ^-12 10 ^4.9

              =10 ^-7.1 W/ m²

                   = 7.94 x10 ^-8 W/ m²