Infinite Point Sources of Sound & The Zeta Function

  • #1

Homework Statement


An infinite number of incoherent sources of sound are located on the x-axis at positions given by n2 (in meters) with n= 1,2,3,4,5... If all the sources emit with a power of 10.0W, calculate the sound level of the total sound wave at the origin. Prove your answer using the Riemann Zeta Function extended to the whole complex plane using analytic continuation.

(This is an April fool's extra problem, it's not going to be marked)


Homework Equations



Riemann Zeta Function
ITotal=I1+I2+2sqrt(I1I2)
Where I is the intensity

The Attempt at a Solution



I can see that their distances increase exponentially, and so I'm trying to make the inverse square law for sound fit in somewhere. Also, I can see that this could create a plane source, given by an integral of all my point sources (Infinitely many).

But honestly I have little experience with the Zeta Function and I don't see the relation with this problem (Wouldn't be surprised if there wasn't a connection)

It's obviously a joke, but I'm still interested in the solution, so any help is appreciated!
 

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