Question 79253
The intensity of light and sound both vary inversely as the square of their distance from the source.

1. Suppose you're relaxing one evening with a copy of Twelth Night, and the reading light is placed 5 ft. from the surface of the book. At what distance would the intensity of the light be twice as great?
:
The inverse variation of the square of x:  y = k/x^2 or k/x^2 = y
Let y = 1 (amt of light) and x = 5 ft; find k:
:
k/5^2 = 1
k = 25
:
Find x when y = 2 (twice as much light); k = 25
2 = 25/x^2
2x^2 = 25
x^2 = 25/2
x^2 = 12.5
x = sqrt(12.5)
x = 3.53 ft there will be twice as much light
:
:
2. Tamino's Aria is playing in the background, with the speakers 12 ft away. At what distance from the speakers would the intensity of sound be three times as great?
:
k/x^2 = y
x = 12 ft; y = 1 (sound level); find k
:
k/12^2 = 1
k/144 = 1
k = 144
:
Let the level of sound = 3
3 = 144/x^2
3x^2 = 144
x^2 = 48
x = sqrt(48)
x = 6.93 ft the sound is three times as much