The intensity I of a sound (in watts per square meter) varies inversely with the square of the distance d (in meters) from the sound's source. At a distance of 2 meters from the stage, the intensity of the sound at a Shostakovich opera is about 12 watts per square meter. What is the intensity of the sound, rounded to the nearest hundredth, you hear if you are sitting 15 meters from the stage?

Question

anonymous · Answer

"The intensity I of a sound (in watts per square meter) varies inversely with the square of the distance d (in meters) from the sound's source"

This means that I = C / d^2 for some constant C that we have to figure out. Just plug in the 2 and 12 to figure out the C. Then use the equation with your newly found C to figure out what I is when d is 15

atlas · Answer

I1/I2 =  (d2)^2/(d1)^2        
This is the inverse relationship

atlas · Answer

Substitute and get your values