質問: 物理波與波長頻率問題麻煩一下 1. if a pendulum clock is accurate at sea level, will it gain or lose time when taken to high altitude? why? 2. a small fly of mass 0.25g is caught in a spider's web. the web vibrates predominantly with a frequency of 4 hz a)what is the value of the spring stiffness k for the web? b) at what frequency would you expect the web to vibrate if an inscet of mass 0.50g were trapped? 3.sketch a series of standing waves on a string between two sold points. show the first three harmonics.
回答: 1. lose time 鐘擺週期 t = 2π√(l/g),當鐘擺被移至海拔較高處,則重力變小,即 g' < g,則 t' > t,鐘擺週期將變大,看起來像是擺動速度變慢,由於這種鐘是每擺動一次計時1秒,時間一久,此鐘顯示的時間將愈來愈落後在海平面的鐘。 2. (a) 彈簧簡諧振盪週期 t = 2π√(m/k),亦即頻率 f = (1/2π)√(k/m), 4 = (1/2π)√(k/0.00025) => k = 0.16 nt/kg (b) f ∝ 1/√m => f' = 4 × √(0.25/0.5) = 2.8 hz 3. 駐波的前三倍頻如下圖的上三圖所示: 圖片參考:http://www.phys.unsw.edu.au/jw/graphics/standing.gif 參考資料: http://www.phys.unsw.edu.au/jw/strings.html http://phys.thu.edu.tw/teachers/lin/physics-ch08.pdf 2011-01-09 22:13:14 補充: k值的單位寫錯,應為0.16 nt/m。