The intensity ,i from a point source decreases with the inverse square of the distance, r from the source. suppose that you are listening to your favourite music coming away from a speaker(regarded as a point source and in an open area) placed exactly r1 from you. then you suddenly decide to move away to a new position ,r2 which is exactly twice as far away from the speaker.
calculate by how many decibels ,db does the sound intensity level ,β drop ,when you move twice as far away from the speaker to your new position.

Lake happy times contains 100 km3 of pure water. it is fed by a river at a rate of 50 km3/yr. at time zero, there is a factory on one shore of lake happy times that begins introducing a pollutant to the lake at a rate of 2km3/yr. there is another river that is fed by lake happy times at a rate that keeps the volume of lake happy times constant. this means that the rate of flow from lake happy times into the outlet river is 52km3/yr. in turn, the flow from this outlet river goes into another lake, lake sad times, at an equal rate. finally, there is an outlet river from lake sad times flowing at a rate that keeps the volume of lake sad times at a constant 100 km3 . (a) find the amount of pollutant in lake sad times at the end of 3 months. (b) at the end of 3 months, observers close the factory due to environmental concerns and no further pollu- tant enters lake happy times. how long will it take for the pollutant in lake sad times (found in part (a)) to be cut in half?