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MCAT Physics Question — Sound Level

  • by John
  • Apr 03, 2017
  • MCAT Question of the Day

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?

 

  1. 2
  2. 8
  3. 12
  4. 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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