Pain Threshold - Reducing Intensity

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SUMMARY

The discussion centers on calculating the distance required for the noise intensity of a jet engine to decrease from 130 dB to 62.2 dB, known as the "pain threshold." The intensity is inversely proportional to the square of the distance, as described by the equation I = (dE/dt) / 4π(r^2). The user attempted to apply the formula I2/I1 = A1/A2 = 4π(r1^2)/4π(r2^2) but arrived at an incorrect distance of 30.4 m. Correct manipulation of the equations is necessary to find the accurate distance.

PREREQUISITES
  • Understanding of sound intensity levels in decibels (dB)
  • Knowledge of the inverse square law in physics
  • Familiarity with basic algebraic manipulation of equations
  • Concept of amplitude and angular frequency in wave physics
NEXT STEPS
  • Review the inverse square law and its application in sound intensity calculations
  • Study the relationship between decibel levels and intensity ratios
  • Practice solving problems involving sound intensity and distance
  • Explore the physics of sound waves, focusing on amplitude and frequency
USEFUL FOR

Students studying physics, particularly those focusing on acoustics and sound intensity, as well as educators seeking to explain the concept of pain thresholds in sound levels.

05holtel
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Homework Statement



At a distance of 30 m the noise from the engine of an jet has an intensity of 130 dB.

At this level, you will be in pain and your ears will hurt. That's why this intensity is know as the "pain threshold".

How far do you have to be from a jet (total distance), in order for the noise to drop down in intensity to 62.2 dB, a level comparable to that of a spoken conversation?

Express the result in the unit m, and to three significant figures.

Homework Equations



I think Intensity is proportional to (1/r^2)

I = (dE/dt) / 4pi(r^2)

I=1/2v(w^2)(A^2) where w = the angular frequency and A - the amplitude

The Attempt at a Solution



I am not sure how to manipulate the equations
 
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PLease help


I was trying the formula I2/I1 = A1/A2 = 4pi(r1^2)/ 4pi(r2^2)

I got 30.4 which is wrong
 

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