company with loud machinery needs to cut its sound intensity to 44% of its original level.
By how many decibels would the loudness be reduced? Use the formula L= 1010g
27一
.
Round to the nearest hundredth.
(1 point)
• 3.57 decibels
• 1.58 decibels
• 2.52 decibels
• 1.93 decibels
To find the number of decibels the sound intensity would be reduced by, we need to calculate the difference in decibels between the original sound intensity (L1) and the reduced sound intensity (L2).
The formula given is L = 10 * log10(g), where L is the sound intensity in decibels and g is the ratio of the reduced sound intensity to the original sound intensity.
In this case, g is given as 44% or 0.44.
So, we have L2 = 10 * log10(0.44).
Using a calculator, we find L2 ≈ -3.357 decibels.
To find the difference in decibels, we subtract L2 from L1.
L1 - L2 = 0 - (-3.357) ≈ 3.357 decibels.
Rounding to the nearest hundredth, the loudness would be reduced by approximately 3.36 decibels, which is closest to 3.57 decibels. Therefore, the correct answer is:
• 3.57 decibels