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What approximate change in decibels does an observer experience from a sound source if the observer moves to a new location that is 67% as far from the source?
My answer choices are 23, -23, 40, 2.76, -2.76, 1.94, -1.94, 2.57, -2.57, and 0
I worked out this problem and came up with the following:
db = 10 log(P2/P1) = 10 log (1/0.67)2 = 20 log (1/0.67) = -20 log (0.67) =
+3.479 dB
This isn't one of my choices. Can you please help and advise me what I did wrong? Thank you!
At the new location, because of the inverse square law, the sound intensity will be higher by a factor
I2/I1 = (1/0.67)^2 = 2.23
10 log(10) I2/I1 = 10*0.348 = 3.48 db
I agree with your answer. You did nothing wrong.
To find the approximate change in decibels when the observer moves to a new location that is 67% as far from the sound source, you can use the inverse square law for sound intensity.
The inverse square law states that the intensity of sound decreases proportionally to the square of the distance from the source.
In this case, since the observer moves to a new location that is 67% as far from the source, the distance is reduced to 0.67 times the original distance.
To calculate the change in decibels, you can use the formula:
ΔdB = 10 log (I2/I1)
Where ΔdB is the change in decibels, I1 is the initial intensity, and I2 is the final intensity.
Now, since intensity is directly proportional to the square of the distance, we can write:
I2/I1 = (d1/d2)^2
Where d1 is the initial distance and d2 is the final distance.
In this case, since the final distance is 67% of the initial distance, we have:
d2 = 0.67 * d1
Substituting this into the intensity formula:
I2/I1 = (d1/(0.67 * d1))^2 = (1/0.67)^2
Now we can calculate the change in decibels using the given formula:
ΔdB = 10 log((1/0.67)^2)
ΔdB = 10 log(1.492537)^2
ΔdB = 10 log(2.229)
ΔdB ≈ 10 * 0.348
ΔdB ≈ 3.48
Therefore, the approximate change in decibels when the observer moves to the new location is approximately 3.48 dB.
Now, looking at the answer choices you provided, the closest answer is +3.479 dB, which is consistent with our calculation.