臺灣國際科展

都是氣泡惹的禍

科展類別
臺灣國際科展
屆次
2005年
科別
物理科
學校名稱
臺中縣私立弘文高級中學
作者
陳冠皓、林天健

摘要或動機

在物理馬戲團這本書中提到:「當你泡即溶咖啡或攪拌奶精的時候,用湯匙輕敲杯壁看看,添加奶精後攪拌時,敲擊的聲音與添加前明顯不同,為什麼?」這本書的解答是:「當粉末溶解的時候,藏在粉末裡的空氣就會跑出來。因為空氣裡的音速低於水裡的音速,在空氣與水混合的環境裡,音速也比在水裡低。當水裡不斷有空氣混進去時,這個容器的共振頻率和它裡面的音速有關,所以也會降低。因此你會聽到較低的音調,直到空氣全部跑光。」我們利用指向性麥克風以電腦錄音後以Adobe Audition 軟體分析聲波頻率,覺得這個說法有點問題。例鹽水溶液音速較水高,敲擊時的音調卻較水低。由敲擊一黏於裝水水盆中之空杯,與敲擊杯內裝同一水位之水之杯子,頻率非常接近。告訴我們影響頻率的是靠近杯壁一層有效質量。因鹽水溶液密度較高有效質量較大,所以頻率較低。以密度的觀念檢視裝有溶液之杯子被敲後的頻率是對的。但對杯中有懸浮物就不然,例如流體中含有氣泡,則混合體之密度必定變低,有效質量變小頻率應變高。但實驗發現含有氣泡時頻率是變低的。可見氣泡還有其他的影響力高於密度對音調的影響。 流體的振動應是會壓縮到氣泡,氣泡與流體間之力學交互作用為何會使頻率下降,正是我們要找出的。 The Flying Circus of Physics has a question “As you stir instant cream or instant coffee into a cup of water, tap the side with your spoon. The pitch of the tapping changes radically as the powder is added and during the stirring. Why?” The answer is, “The air trapped in the powder is released as the powder dissolves. Since the speed of sound is lower in air than that in water, the speed of sound in the air-water mixture is lower than that in pure water. During that period while the air escapes the container, the resonant frequencies of the water, which depend directly on the speed of sound, will also be lower. Hence, you hear a lower tone until the air escapes. “We then tap the coffee cup and generate an audible tone. The signal picked up by the microphone . The same signal is also studied using Adobe Audition, a waveform processing and analyzing software. We find the assumption is wrong, the speed of sound is higher in sugar solution than that in water, but we hear a lower tone. An effective layer of fluid adjacent to the glass wall is set into motion when we gently rub the rim of the wineglass. The thickness is about the same whether the fluid is inside or outside the glass. This explains why the frequency drops when the liquid is added to the system. When the density of the sugar solution is higher, the mass of the effective layer is higher. But what the presence of the bubbles and the theoretical explanations must NOT rely on are: Use effective density argument: One should not just use a change in the main density to try to explain why the frequency is lower. I would think that the bubbles are compressed a little bit by the vibrational motion of the glass communicated to them through the fluid. But how do the bubbles interact with the fluid under this setting? This is what we need to work out.


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