The intensity level of the sound 20.0 meters from a jet is 120. dB. a) Calculate

Question

The intensity level of the sound 20.0 meters from a jet is 120. dB.
a) Calculate the intensity of the sound 20.0 meters from the jet.
b) Sam is standing 20.0 meters from the jet listens to the jet engine for 3.00 minutes.
Calculate the energy reaching Sam’s eardrums during the three minutes he listened to
the jet engine. The average adult eardrum has a surface area of about 2.10x10-3 m2.
c) Calculate the average power of the sound produced by the jet engine.
d) Calculate the intensity of the sound 60.0 meters from the jet.
e) Calculate the intensity level of the sound 60.0 meters from the jet.

Explanation / Answer

Here is my reasoning: Sound intensity level in dB of a sound with intensity I is defined as: L = 10·log10(I/I0) where I0 = 10?¹²W/m² is the threshold of hearing. That means a barely audible sound - intensity I0 - has the intensity level: L = 10·log10(1) = 0dB Since soundwave propagate spherically the sound power of the source at the distance r to is uniformly distributed over the surface of a sphere with radius r, which is 4·p·r². Therefore sound intensity is inversely proportional to the squared distance to the source: I ~ 1/r² So the ratio of two sounds at different distances is I2/I1 = (r1/r2)² Such a ratio can be expressed as difference of the intensity levels: ?L = L2 - L1 = 10·log10(I1/I0) - 10·log10(I2/I0) because log(a) - log(b) = log(a/b) ?L = 10·log10(I1/I2) So the level difference between two distances from the source is: ?L = 10·log10((r1/r2)²) = 20·log10(r1/r2) Knowing the distance r1 you can calculate the distance at which SIL has changed by ?L: r2 = r1/10^( ?L/20) = r1·10^( -?L/20) = r1·10^( (L1 - L2)/20 ) For this problem r1 = 20m L1 = 120dB L2 = 100dB => r2 = 20m · 10^( (120 - 100)/20 ) = 20m · 10^( 1 ) = 200m

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