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

Adding five equally loud sources of sound will increase the sound level by 7.8 dB. Therefore, the total sound level can be calculated as:
60 dB + 7.8 dB = 67.8 dB
However, the threshold of hearing is given as 1.0 × 10-12 W/m2. Therefore, we need to convert the sound level to the corresponding intensity level in W/m2 using the following formula:
IL = 10 log (I/I0), where I0 is the threshold of hearing
Rearranging this formula, we get:
I = I0 × 10IL/10
Substituting IL = 67.8 dB and I0 = 1.0 × 10-12 W/m2, we get:
I = 10-12 × 106.78/10 = 10-12 × 501.1872 = 7.943 × 10-7 W/m2
Now we can convert this intensity level back to the corresponding sound level in dB using the formula:
SL = 10 log (I/Iref), where Iref is a reference intensity of 1.0 × 10-12 W/m2
Substituting Iref = 1.0 × 10-12 W/m2 and I = 7.943 × 10-7 W/m2, we get:
SL = 10 log (7.943 × 10-7/1.0 × 10-12) = 10 log 7.943 + 10 log 106 = 67 dB
Therefore, the total sound level you are being exposed to is 67 dB. The correct answer is D.

The Sound Level at 1