Sound Intensity: Thresholds of Hearing & Ratio Calculation

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SUMMARY

The discussion centers on calculating the ratio of sound intensities I1 and I2 based on the thresholds of hearing for two individuals, Person 1 with a threshold of β1 = -5.00 dB and Person 2 with β2 = +12.0 dB. The reference intensity is set at 1 × 10-12 W/m2, where 0 dB corresponds to this intensity. The equation used, 12 - (-5) = 10 * log(I2/I1), leads to the conclusion that I2/I1 equals 50.12. However, the correct ratio I1/I2 is the inverse of this value, which is approximately 0.0199.

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  • Understanding of sound intensity and decibel scale
  • Familiarity with logarithmic calculations
  • Knowledge of the relationship between sound intensity and thresholds of hearing
  • Basic algebra skills for manipulating equations
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  • Review the concept of sound intensity in the context of the decibel scale
  • Study logarithmic functions and their applications in sound calculations
  • Learn about the thresholds of hearing and their significance in acoustics
  • Practice solving problems involving ratios of sound intensities
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Homework Statement


Using an intensity of 1 × 10-12 W/m2 as a reference, the threshold of hearing for an average young person is 0 dB. Person 1 and person 2, who are not average, have thresholds of hearing that are β1 = -5.00 dB and β2 = +12.0 dB. What is the ratio I1/I2 of the sound intensity I1 when person 1 hears the sound at his own threshold of hearing compared to the sound intensity I2 when person 2 hears the sound at his own threshold of hearing?


Homework Equations


12 - (-5) = 10 * log(I2/I1)


The Attempt at a Solution


17 = 10 * log(I2/I1)
1.7 = log(I2/I1)
I2/I1 = 10^1.7 = 50.12

I submitted this online and it says it is incorrect. Anyone able to see where I went wrong?
 
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I1/I2 is the question.

ehild
 

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