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

Question

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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=

Mathematics

1 answer:

Natasha2012 [34] · Answer 1 · 2022-03-17T10:50:38+03:00

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