Response of a Vibrating Plate in a Fluid 



With the use of the asymptotic form of the Hankel function, the 

 asymptotic form of ijj may be computed. This form is 



j kr(Vl-M^sin^f Mcosg ) 



,, Q, A(e)e ^ •' 



^ °° V2Trikr Vl - M^ sin^ 9 



where 



• '<*V <^°s B \ 



A(e) = \ dx'e ^ W(x') 



The acoustic velocity in the radial direction u^ is given by 



u,=|i(r,e) 



_ ik(Vl - M^ sin^ 9 + M cos 9) .. q. 

 M^ - 1 



The pressure, p, a microphone in the far-field would measure is 

 given by 



^ P = iki|j - M 

 = Ikilj - 



pc ^ 9x 



IkM^ 



M^- 1 



= ^H(r,9) 

 M^ - 1 



The average radiated intensity is given by the expectation value 



I = iRe^pu*> 



ikpc ik(Vl - M^ sin^ 9 + M cos 9) J_ ^^ . ^^*. 

 M^ - 1 M^ - 1 2 



= pck^(Vl - M^ sin^ 9 + M cos 9) ^^ ^ ^^*^ 



2(m2 - 1)^ 



Now, 



597 



