High-Frequency Underwater Acoustic Propagation in a Port Modeled as a Three-Dimensional Duct Closed at One End Using the Method of Images

<table>Three-Dimensional Distribution of Images between Pressure Release Boundary <svg height="15.25" id="M122" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 19 15.25" width="19" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,11.113)"><path d="M703 650v-28q-62 -4 -76.5 -20t-14.5 -76v-402q0 -60 14 -76t74 -20v-28h-266v28q63 4 78 20t15 76v459q0 20 -6 25t-27 5h-249q-23 0 -28.5 -5.5t-5.5 -26.5v-457q0 -60 14 -76t72 -20v-28h-257v28q58 4 72 20.5t14 75.5v402q0 61 -14.5 76.5t-75.5 19.5v28h667z" id="x3A0"></path></g>
<g transform="matrix(.012,0,0,-.012,12.613,15.188)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg> and Soft Boundary <svg height="15.25" id="M123" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 19 15.25" width="19" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,11.113)"><path d="M703 650v-28q-62 -4 -76.5 -20t-14.5 -76v-402q0 -60 14 -76t74 -20v-28h-266v28q63 4 78 20t15 76v459q0 20 -6 25t-27 5h-249q-23 0 -28.5 -5.5t-5.5 -26.5v-457q0 -60 14 -76t72 -20v-28h-257v28q58 4 72 20.5t14 75.5v402q0 61 -14.5 76.5t-75.5 19.5v28h667z" id="x3A0"></path></g>
<g transform="matrix(.012,0,0,-.012,12.613,15.188)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>, Group <i>m = </i>0.</table>

Advances in Acoustics and Vibration

fig6

Figure 6

Figure 6: High-Frequency Underwater Acoustic Propagation in a Port Modeled as a Three-Dimensional Duct Closed at One End Using the Method of Images 