摘要或動機

可聽聲有向四周擴散繞射特性，而超聲波具有指向性，改以超聲波載送可聽音訊號後，其載波與旁頻帶均在超聲波範圍，實驗中人耳卻可聽到高度指向性聲音，且調幅解調後的可聽聲衰減率比純超聲波來的低。那為什麼超聲波會解調可聽音？我們以非線性的數學轉換概念，成功以數學推導解釋實驗中所聽到的可聽聲，是由旁頻經由非線性轉換而來的。為了證實空氣中的超聲波有非線性現象，以發射40KHz單頻訊號，除了接收到40KHz訊號外還可接收80KHz訊號，而80KHz訊號振幅，會隨著發射強度而遞增，也會隨著傳輸距離增加至穩定狀態，這所我們從文獻中的非線性理論所吻合。接下來進行調幅超聲波實驗，我們經理論計算旁頻帶強度為頻率響應與調變率乘積的一半，而解調可聽聲的強度為調變率、頻率響應與非線性係數三者乘積，我們也由實驗數據證實理論計算結果，在實驗中，換能器在40KHz有最佳的頻率響應，其非線性係數與所載送可聽聲頻率高低約略成正相關，並且與換能器距離遞增而越遠而增加。此外在提高高指向可聽音輸出功率方面，除製作專屬的放大器、運用方波取代正弦波來載波、配合陣列換能器輸出；在改善音質方面，利用等化器調整訊源頻譜分佈，降低低頻振幅，增強高頻振幅，讓各頻率的原始訊號都能有適當的調變，達到最佳音質。The audible sound has the characteristics of spreading and diffracting. And ultrasonic is directive. We modulate sound into ultrasonic signal. The carrier and sideband are ultrasonic frequency bands. But in the experiment, human can hear highly directive sound. In terms of attenuation rate, AM demodulation sound is lower than pure ultrasonic wave. Why can human hear the directive sound? By using the nonlinear mathematical transform, we managed to explain the audible sound which is transformed from sideband with nonlinear effect in the experiment. In order to confirm that nonlinear phenomena in the air ultrasonic, we launch 40KHz single tone ultrasonic signal. Besides the 40KHz signal, we also received 80KHz signal. The amplitude of 80KHz signal will increase with the emission intensity, and also with the transmission distance to increase its stability. These are consistent with nonlinear theory in the literature. Next we began AM ultrasonic experiment. We calculated the sideband intensity that is the product of frequency response and modulation index. The demodulation sound intensity is the product of modulation index, frequency response, and nonlinear coefficient. We also proved the calculated consequence through the experiment. In the experiment, the ultrasonic transducer has a best frequency response in 40KHz. The nonlinear coefficient has positive correlation with the modulation frequency, and increases transmission distance. To boost the power of directive audible sound, we made an amplifier, using square wave to replace sine wave of carrier, and in conjunction with array transducer output. To improve the sound quality, We use the spectrum-Equalizer to adjust the frequency distribution of the origin signal. The EQ reduces the low-frequency amplitude, and boost high-frequency amplitude, which enables every frequency of the original signal to be properly modulated, achieving the best sound quality.