The sound level can be determined using the equation, dB = 10log10(I/Io), where dB is the sound level measured in decibels, I is the intensity of the sound measured in W/m2, and Io (W/m2) is the threshold of hearing in a healthy human. How many orders of magnitude greater is the intensity of sound measured at 120 decibels compared to a sound of 40 decibels?
- 2
- 8
- 12
- 80
Click for Explanation
This question requires the examinee to understand the logarithmic relationship between the sound level and intensity. As a general rule, an increase in 10 dB corresponds to an increase in intensity by a factor of 10. Therefore, the 80-decibel difference in sound levels in this problem corresponds to a difference in intensity by a factor of 108.
dB = 10log10(I/Io)
120 = 10log10(I120/Io)
12 = log10(I120/Io)
I120 = Io1012
dB = 10log10(I40/Io)
40 = 10log10(I40/Io)
4 = log10(I40/Io)
I40 = Io104
I120/I40 = Io1012/Io104
I120/I40 = 108
Thus, the intensity of the sound at 120 decibels is eight orders of magnitude greater than sound at 40 decibels making B the correct answer.
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