SOLUTION: The loudness of a stereo speaker, measured in decibels, varies inversely as the square of the distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 de

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The loudness of a stereo speaker, measured in decibels, varies inversely as the square of the distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 de      Log On


   

Question 1208725: The loudness of a stereo speaker, measured in decibels, varies inversely as the square of the distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you’re 4 feet from the speaker?
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


A somewhat informal solution.... I will leave it to other tutors to provide a more formal solution if they want to.

The ratio of distances is 1:2,
so the square of the ratio of distance is 1:4,
so, because it is an inverse variation, the ratio of sound levels is 4:1

(28)*4 = 112

ANSWER: 112 db

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 112 decibels

Explanation

x = distance you are from the speaker
y = decibel level

The loudness varies inversely as the square of the distance from the speaker.
That gives us this equation
y+=+k%2F%28x%5E2%29
As x gets bigger, y will get smaller, and vice versa.

Let's find k when x = 8 and y = 28
y+=+k%2F%28x%5E2%29
28+=+k%2F%288%5E2%29
k+=+28%2A8%5E2
k+=+1792
Therefore the equation is
y+=+1792%2F%28x%5E2%29

If you are x = 4 feet from the speaker, then,
y+=+1792%2F%28x%5E2%29
y+=+1792%2F%284%5E2%29
y+=+112
112 decibels is the final answer.


This level of loudness is somewhere between a loud night club (110 dB) and operating heavy equipment (120 dB).

Image Source:
https://www.osha.gov/noise
Scroll down to the "Exposure & Controls" subsection.
Then click on "how loud is too loud?" to see the chart shown above.