Acoustic Topography Varying with the Position of the Organ by Barus C.

By Barus C.

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Znstr. Methods 176 (1980) 381. 4 Method 111:Direct Integration 49 where p, satisfies the following relation involving the special functions J and Y known as Bessel and Neumann functions: Jo(pna)Yo(pnb)- Jo(pnb)Yo(pLna) = 0. Which condition determines the coefficients K,, and which the coefficients B,? Solution: For the detailed solution we refer this time t o the literature cited above. 4 Method 111: Direct Integration In this case one integrates either vectorially, as in ~ = JF, k or scalar-wise as in 4 =k J dq=pdV, dqr.

Show that the potential 4(r,z ) in this intermediate space obtained with the following boundary conditions is given by *See also for instance Greiner [ 4 ] ,p. 29. +H. Sipila, V. Vanha-Honko and J. Bergqvist, Nucl. Znstr. Methods 176 (1980) 381. 4 Method 111:Direct Integration 49 where p, satisfies the following relation involving the special functions J and Y known as Bessel and Neumann functions: Jo(pna)Yo(pnb)- Jo(pnb)Yo(pLna) = 0. Which condition determines the coefficients K,, and which the coefficients B,?

K J S(r - r’)47rp(r’)dr’= -4k7rp(r). e. 12) = -47rS(r). 13) This express,m makes sense only for r # 0. Now, r = Jx2+ y 2 + 22, d2 d2 d2 ax2 ay2 az2 A = -+ - + - and 1 X 3x2 so that 3r2 = 0. 13) is correct: /Aldr= Jv =-s,; / V . V - d1 r = Jv - . dF 1 JF r dF J T2 = - J d o = -4T. This verifies Eq. 13). 12) shows that the Green’s function is the potential of a negative unit charge at the source point multiplied by €0 since with p(r’) = -q,S(r’) 20 CHAPTER 2. ELECTROSTATICS we have #(r’) = -k J - BASIC ASPECTS G(r - r’)4~p(r’)dr’= G(r).

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