A noisy workplace has a noise level of 90 dB.You want to reduce this to a more comfortable 75 dB.By what factor must the power of the noise source be reduced? (That is,what is the ratio of the new power to the old?)
A)0.83
B)0.67
C)0.32
D)0.032
E)0.010

Question

Quizplus · Accepted Answer

The sound level in decibels is calculated using the formula $L = 10 \log_{10}(\frac{P_1}{P_0})$, where $L$ is the sound level in decibels, $P_1$ is the power of the sound, and $P_0$ is a reference power. To find the factor by which the power must be reduced, we use the difference in decibels: $75 dB - 90 dB = -15 dB$. The equation becomes $-15 = 10 \log_{10}(\frac{P_{new}}{P_{old}})$. Solving for $\frac{P_{new}}{P_{old}}$ gives us a factor of approximately 0.032, meaning the power must be reduced by this factor to achieve the desired decrease in noise level.

A Noisy Workplace Has a Noise Level of 90 DB