Calculating Energy Received by a Human Eardrum at Threshold of Hearing

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SUMMARY

The discussion focuses on calculating the energy received by a human eardrum at the threshold of hearing, specifically using the intensity of sound at 1.04E-12 W/m². The radius of the eardrum is given as 4.10 mm, which converts to 0.0041 m. The area of the eardrum is calculated using the formula A = πr², resulting in an area of approximately 0.000211 m². The power (P) is then derived from the intensity equation I = P/A, leading to the conclusion that the power received by the eardrum can be accurately determined using these calculations.

PREREQUISITES
  • Understanding of sound intensity and its measurement in watts per square meter (W/m²).
  • Knowledge of basic geometry, specifically the area of a circle (A = πr²).
  • Familiarity with the relationship between power, energy, and time in physics (P = E/t).
  • Ability to perform unit conversions, particularly from millimeters to meters.
NEXT STEPS
  • Study the principles of sound intensity and its effects on human physiology.
  • Learn more about the physics of sound waves and their propagation.
  • Explore the concept of thresholds in sensory perception, particularly in hearing.
  • Investigate the relationship between power and energy in different physical contexts.
USEFUL FOR

Students studying physics, audiologists, and anyone interested in the mechanics of human hearing and sound perception.

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Homework Statement


The radius of a typical human eardrum is about 4.10 mm. Calculate the energy per second received by an eardrum when it listens to sound that is at the threshold of hearing, assumed to be 1.04E-12 W/m^2.


Homework Equations


I=P/A


The Attempt at a Solution


First i start by converting 4.10mm to m, for which i get .0041m.

The rest seems simple:
Intensity= 1.04E-12 W/m^2
Area= 4(pi)(r^2)

plugging in my numbers i get 1.04E-12 W/m^2= P/.000211

Then I solve for P, because power=Energy per time and is expressed in W.
This problem seems like it should be simple. I really have no idea where i am making the mistake, any help would be greatly appreciated.
 
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I'm assuming the eardrum is roughly circular. Hence:

A = \pi r^2
 
Thanks for the help, that's what i was doing wrong :)
 

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