The loudness of a sound (measured in decibels dB) is inversely proportional to the square of the distance from the source of the sound. Suppose a person who is 3 ft from a hair dryer experiences a sound level of 75 dB. Find the proportionality constant and write the equation that expresses the inverse proportionality.

Question

The loudness  of a sound (measured in decibels dB) is inversely proportional to the square of the distance  from the source of the sound. Suppose a person who is 3 ft from a hair dryer experiences a sound level of 75 dB. Find the proportionality constant and write the equation that expresses the inverse proportionality.

Quizplus · Accepted Answer

According to the problem, we know that the loudness (L) is inversely proportional to the square of the distance (d) from the source. Mathematically, we can write:
L = k/d^2
where k is the proportionality constant. To find k, we can use the given information that when the person is 3 ft from the hair dryer, the sound level is 75 dB. Substituting in the formula above, we get:
75 = k/3^2
Simplifying, we get:
k = 75*9
k = 675
Therefore, the equation that expresses the inverse proportionality is:
L = 675/d^2
which can be written as:
d^2 = 675/L

The Loudness of a Sound (Measured in Decibels DB)