Sound intensity/Ear drum problem

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Homework Help Overview

The problem involves sound intensity and the relationship between power, intensity, and distance from a sound source. The original poster presents a scenario where sound waves are emitted isotropically, and calculations are required to determine the power of the source and the distance needed for a specific energy reception by the ears.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster outlines a method to solve for the power of the source and the distance required for energy reception, questioning the validity of their approach regarding the area calculation for both ears.
  • Some participants question the assumptions made about the time period for energy reception and suggest clarifying the problem statement.
  • Others confirm the need to double the area when considering both ears.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's reasoning and clarifying points about the problem's requirements. There is a recognition of the need to adjust calculations based on the energy per second specification.

Contextual Notes

Participants note that the problem may lack clarity regarding the time period for energy reception, which could affect the calculations. The original poster is also considering how to account for both ears in their area calculations.

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Homework Statement


A source emits sound waves equally in all directions. The intensity of the waves 2.50m from the source is 1.9 * 10^-4 W/m^2
a) Find the power of the source
b) If the diameter of your ear drum is 8.4 mm, how far from the source do you have to be located, so that your ears combine receive 0.42*10^-12 Joules of energy.

Homework Equations


Intensity = Psource/(4πR^2) Due to it being an isotropic source
Preceived = (Intensity)/(Area)
Energy = (Preceived) * (time)

The Attempt at a Solution


So part (a) I'm easily able to solve using the formula, Intensity = Psource/(4πR^2)
Just plug in the value for the intensity and distance (2.50m), isolate for Psource, and you get .015 Watts.

Part (b) I'm pretty confident I know how to solve, there are just a few things that are tripping me up. What I would do is
1) Energy = (Preceived) * (time) From this you are able to determine the Preceived is 0.42*10^-12 Watts, by simply plugging in 1 second for time.
2) You would then use Preceived = (Intensity)/(Area). Using the diameter of the ear given, we are able to solve for the area: (π(4.2*10^-3 m)^2). Plug in the value from Preceived and get the Intensity.
3) Plug this Intensity value, along with Psource from part (a) into the formula, Intensity = Psource/(4πR^2)
and then solve for R. Am I right in determining that the 'R' in this formula would represent the distance we are trying to determine?

Can someone confirm this process is correct?
The issue that I am running into is that the question asks how far you have to be so that BOTH your ears combined receive 0.42*10^-12 Joules of energy. From our calculations, we only took into account the area for one ear. Do I double the area for the ear for the prior step then solve? Or can I just halve the power and then solve for one ear? I'm so confused.
 
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Where do you get the period of 1 second from? Seems to me the question is flawed. It should either specify a period of time or specify a level of received power, not a quantity of energy.
Other than that, yes, just double the area.
 
Oh yeah. Forgot to add that the question says 0.42*10^-12 Joules of energy per second.
Would my calculations now be correct?
 
Zeus711 said:
Oh yeah. Forgot to add that the question says 0.42*10^-12 Joules of energy per second.
Would my calculations now be correct?
Should be.
 

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