Although the generalized radiation impulse response approach is applicable for interior and exterior radiation problems, it is noted that Eqs. (38) and (40) are, in general, applicable for exterior radiation problems but not for interior radiation problems. A simple example to illustrate the point for interior radiation problems is a piston at the end of a fluid filled semi-infinite rigid walled duct, where

z(τ)=ρ0c0Ayδ(τ).

Clearly, Eqs. (38) and (40) are not satisfied since h(τ)=0.

The correction can be simply noted in the paper1 by modifying the line preceding Eq. (38) to include “for exterior radiation problems” as follows:

Zn(ka)zn(τ)
(37)

and Zn(0)=0 from Eq. (16) for exterior radiation problems, it is then apparent that

z(τ)dτ=0.
(38)

Also, since

H(ka)h(τ)
(39)

it then follows that H(0)=1 and

h(τ)dτ=1.
(40)
1.
Peter R.
Stepanishen
, “
Acoustic time-dependent energy from vibrating surfaces via a generalized radiation impulse response approach
,”
J. Acoust. Soc. Am.
148
(
3
),
1296
1303
(
2020
).