Sound level: The sound level at 1.0 m from a certain talking person talking is 60 dB. You are surrounded by five such people, all 1.0 m from you and all talking equally loud at the same time. The threshold of hearing is 1.0 × 10^-12 W/m². What sound level are you being exposed to? You can neglect any absorption, reflection, or interference of the sound. The threshold of hearing is 1.0 × 10^-12 W/m². A) 300 dB B) 60 dB C) 74 dB D) 67 dB E) 81 dB

Question

Quizplus · Accepted Answer

The sound level follows the logarithmic scale, so we cannot simply add up the dB values. Instead, we can use the formula:

Lp1 + Lp2 + ... + Lpn = 10 * log10(I1 + I2 + ... + In)

where Lp is the sound level in dB and I is the sound intensity in W/m^2.

In this case, n = 5 and the distance from each person to you is the same, so the sound intensity from each person is the same:

I1 = I2 = ... = In = (10^-12) W/m^2 (based on the threshold of hearing given)

Plugging in the values, we get:

60 dB + 60 dB + 60 dB + 60 dB + 60 dB = 10 * log10(5*(10^-12) W/m^2)

300 dB = 10 * log10(5*(10^-12) W/m^2)

30 dB = log10(5*(10^-12) W/m^2)

10^30 dB = 5*(10^-12) W/m^2

dB = 10 * log10(5*(10^-12) W/m^2) = 67 dB

Therefore, you are being exposed to a sound level of 67 dB.

Sound Level: the Sound Level at 1