過去數十年來各式各樣海中活動大量增加，這些活動會造成各種的海洋環境噪音，這些噪音經研究被認為會對海洋生物造成潛在危害與威脅。由於全球資源短缺，許多國家已發展各項替代能源，其中離岸風力發電於風力能源項目中扮演重要角色，然而離岸發電風車底座之建造於打樁時會在水下環境產生高分貝噪音。為減低施工噪音，前人應用聲音通過氣泡幕衰減之特性，於打樁處周圍設置環形氣泡幕。Commander及Prosperetti (1989)已發展有效的一維平面聲波通過氣泡幕之理論公式。為模擬實際聲音通過環形氣泡幕情形，本研究參照前人理論，並假設聲源為單頻球面波通過環形氣泡幕，發展三維理論公式，且經實驗值與理論值比較，整體上具一致性。

The diversity and amount of marine activities in oceans has increased over the past few decades, and these activities generate intense sound into the marine environment, which has been identified as a potential threat to marine mammals. Due to global energy shortages, many countries have developed methods to make use of renewable energy, and while the development of offshore wind energy is likely to play a major role in this, the pile driving needed when laying the foundations of wind turbines in water produces high sound levels in the underwater environment. In order to mitigate underwater noise, piles being driven into a seabed are usually surrounded by curtains of freely rising air bubbles. Commander and Prosperetti (1989) developed an effective theory of one-dimensional plane wave propagation through bubbly liquid. To model the real underwater sound source surrounded by air bubble curtains, in this work we develop a three-dimensional mathematical model. We assume that the sound is a spherical monochromatic wave from a point source, which propagates through a circular air bubble curtain. A comparison of the results of the theory and experimental data show that the values are overall in agreement.

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