A20B-0008-0540
A20B-0008-0540
按照前面講的相對伸長量決定勢能的規(guī)律,這段原長為 的質(zhì)元現(xiàn)儲存的勢能為
如果將右側(cè)的 移到左邊相除,則得到的是該段介質(zhì)內(nèi)的平均勢能密度 ,故 仿照平均速度到瞬時速度的過渡方式——將時間 得到任意時刻的速度,現(xiàn)在考慮小的一段介質(zhì),上式中的 ,無窮小量變成微分量,用 代替 ,則得介質(zhì)中任意點的勢能密度為
看到了吧!兩個微分相除導(dǎo)致微商,這樣就得到導(dǎo)數(shù)了。
實際上,考慮任意時刻的情形, 是 和 的函數(shù) ,故應(yīng)用偏導(dǎo)符號 代替 重寫為 這下好了!誰的導(dǎo)數(shù)?偏移量 對質(zhì)元坐標(biāo) 的偏導(dǎo)數(shù),也就是質(zhì)元的偏移量對坐標(biāo)的變化率!這不就是波形曲線上某一點切線的斜率嗎?
所以,媒質(zhì)中質(zhì)元的勢能取決于波形曲線上的切線的斜率,斜率值越大,勢能越大,值越小,勢能就越小。
很顯然,波形曲線上,平衡位置處的斜率值大??!所以這個位置的勢能大!什么地方斜率為零?當(dāng)然就是波峰和波谷處,所以這些位置的勢能為零!
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