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

Answer 2

a. The formula for Q as a function of n is $Q\; \alpha \;\frac{1}{n^2}$

b. The value of the constant of proportionality, k, is 11,952.

Given the following data:

• Volume, Q = 83 decibels

• Distance, n = 12 meters

To write a formula for Q as a function of n, and finding the value of any unknown constants.

Mathematically, the inverse relationship between the volume, Q, of a sound and the square of the distance n, in meters, is given by the formula:

$Q\; \alpha \;\frac{1}{n^2}\\\\Q = \;\frac{k}{n^2}$

Next, we would determine the constant of proportionality:

$83 = \frac{k}{12^2} \\\\83 = \frac{k}{144}\\\\k = 83 \times 144$

Constant, k = 11,952

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