An audio engineer takes decibel readings at distances of r1 = 11 m and r2 = 21 m from a concert stage speaker during a sound check. When he is r1 from the speaker, the engineer registers a decibel level of β1 = 110 dB on his loudness meter.

r1 = 15 m
r2 = 21 m
β1 = 101 dB

a. What is the intensity of the sound, I1, in watts per square meter, that is measured by the loudness meter when the engineer is a distance of r1 from the speaker?
b. How much power P, in watts, is coming from the speaker during the sound check at distance r1?
c. Assuming that the speaker output does not change between the two measurements at r1 and r2, what sound intensity level β2, in decibels, will the loudness meter report when the engineer is at a distance r2 from the speaker?

a)

b)

c)

Explanation:

r1 = 15m

r2 = 21m

β1 = 101 dB

Calculating intensity I1 on the loudness meter using the equation:

 a)            

              (corresponding to β=0)

⇒          

⇒          

⇒          

⇒           ×

⇒        

b)      Power

  where is the area of sphere of radius r1

⇒              

⇒              

⇒                

c)      

⇒      

    Simplifying

⇒      

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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i think it would be 5