【基本概念】

1 號筒（horn）

   （電聲詞典）它亦稱“喇叭（筒）”。截面積在長度方向逐漸變化的聲管。用于改進振膜與空氣負載的匹配，還可以調節號筒揚聲器的指向性。

2 指數號筒（exponential horn）

   截面積隨縱向位置呈指數增長的一種號筒。它提供了較為均勻的輻射特性和較寬的頻率響應范圍。

3 擴張常數（flare constant）

   它是指喇叭橫截面的形狀參數，用于描述喇叭的逐漸擴大或收縮的程度。

   喇叭的橫截面可以是各種形狀，如圓形、拋物線形、指數形等。這些不同的形狀會對喇叭的聲學特性產生影響。喇叭的擴張常數是其中一個重要的參數，它決定了喇叭橫截面的變化速率。在指數喇叭中，擴張常數表示喇叭橫截面的幾何級數增長率。具體來說，如果喇叭的截面積隨著距離喇叭口越來越遠而以指數函數的形式增大，那么擴張常數就是這個指數函數的底數。較大的擴張常數表示喇叭的橫截面變化更為急劇，喇叭的聲壓級分布也會相應改變。通過調整喇叭的擴張常數，設計師可以控制喇叭的頻率響應、指向性和功率傳輸等聲學特性。一般來說，較小的擴張常數可使喇叭具有更廣的頻率響應范圍，但指向性較差；而較大的擴張常數則可以提供更好的指向性，但可能限制頻率響應的范圍。

4 喇叭的截止頻率（horn cutoff frequency）

   它是喇叭能傳播有效聲音的最低頻率。在該頻率以下，喇叭無法有效傳輸聲音。它是與喇叭的尺寸、形狀和設計參數等因素相關的重要參數。

【正文】

Although there are numerous mathematical treatments of horns in the texts on acoustics, they all suffer from a common set of inadequacies: the models developed in the literature account for energy transmission inside the horn, but there are no closed-form solutions to the problem of horn directivity—i.e., the behavior of a horn’s radiation outside the boundaries of the horn walls, where listeners are located. Modern horn designers have been far less concerned with optimizing acoustic loading than with creating desirable directivity characteristics, and the designs have without exception been derived empirically rather than analytically.

   In an exponential horn, the cross-sectional area is given by

   where,

   S₀ is the cross-sectional area at the horn’s throat, or entry,

   m_x is called the flare constant.

   The radiation impedance of an exponential horn, assumed to be infinitely long for our purposes, is

   The first term in the brackets is the radiation resistance, and the second is the radiation reactance. Of interest is the frequency at which the value of expression inside the square root becomes zero

   This is known as the horn cutoff frequency. The above theory predicts that no sound will be transmitted through the horn below this frequency. Clearly, this is not the case with real horns, so the theory contains one or more assumptions that are not met in practice. Note also that the second term in the brackets, the radiation reactance, goes to zero in the high-frequency limit.

【Reference】

《Electroacoustic Devices: Microphones and Loudspeakers》Edited by Glen Ballou

《電聲詞典》第二版

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文章來源：大平聲學網