A sound meter placed 5.0 m away from a speaker registers a sound level of 60 dB.If the volume on the speaker is turned down so that the power is reduced by a factor of 40,what will the sound meter now read?
A)1.5 dB
B)7.5 dB
C)15 dB
D)44 dB
E)56 dB

Question

Quizplus · Accepted Answer

The sound level in decibels (dB) can be calculated using the formula: $L = 10 \log_{10} \left(\frac{I}{I_0}\right)$, where $L$ is the sound level in dB, $I$ is the intensity of the sound, and $I_0$ is the reference intensity, typically the threshold of hearing. When the power of the sound source is reduced by a factor of 40, the intensity of the sound is also reduced by a factor of 40 because power and intensity are directly proportional in this context. The change in sound level, $\Delta L$, due to a change in intensity can be calculated using the formula: $\Delta L = 10 \log_{10} \left(\frac{I_1}{I_2}\right)$, where $I_1$ and $I_2$ are the initial and final intensities, respectively. Substituting the given reduction factor into the formula gives: $\Delta L = 10 \log_{10} \left(\frac{1}{40}\right) = -16 \text{ dB}$. Therefore, the new sound level is $60 \text{ dB} - 16 \text{ dB} = 44 \text{ dB}$.

A Sound Meter Placed 5