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
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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) (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) (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
As x gets bigger, y will get smaller, and vice versa.
Let's find k when x = 8 and y = 28
Therefore the equation is
If you are x = 4 feet from the speaker, then,
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.
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