Question

The volume, Q, of a sound is inversely proportional to the square of the distance n, in meters, from the source of the sound. A sound is heard at 83 decibels at a distance of 12 meters from its source. Write a formula for Q as a function of n, including finding the value of any unknown constants. Q=

Answer 1

Answer:

Q = 83n²/144

Step-by-step explanation:

The volume, Q, of a sound is inversely proportional to the square of the distance n, in meters, from the source of the sound

This means that

Q ∝ n² where K is the constant of proportionality in Decibels/meters²

Q = Kn²

if a sound is heard at 83 decibels at a distance of 12 meters from its source, then

83 = K(12²)

K = 83/144 (in Decibels/meters²)

Hence

Q = 83n²/144