1. PhysicsNTHU MFTai- 戴明鳳 Lab. 8A - String Vibration ( 弦振盪 ) Standing wave in stationary medium. The red dots represent the wave nodes.nodes http://en.wikipedia.org/wiki/Standing_wave

2. I. Object ( 目的 ) To obersve that a vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note. Vibrating strings are the basis of any string instrument like guitar, cello, or piano. vibrationstring wavesoundfrequencypitch note string instrument guitarcellopiano VibrationVibration and standing waves in a string, The fundamental and the first 6 overtones.fundamentalovertones http://en.wikipedia.org/wiki/Standing_wave

3. PhysicsNTHU MFTai- 戴明鳳 Vibrating String The fundamental vibrational mode of a stretched string is such that the wavelength is twice the length of the string.fundamental The basic wave relationship and wave velocity are givenwave relationshipwave velocity The string will also vibrate at all harmonics of the fundamental. Each of these harmonics will form a standing wave on the string.harmonics standing wave

4. PhysicsNTHU MFTai- 戴明鳳 An ideal vibrating stringstring Will vibrate with its fundamental frequency and all harmonics of that frequency.fundamental The position of nodes and antinodes is just the opposite of those for an open air column.nodesair column The fundamental frequency The harmonics are integer multiples.

5. PhysicsNTHU MFTai- 戴明鳳 A resonant standing wave on a soft string. It is driven by a vibrator at 120 Hz. For strings of finite stiffness, the harmonic frequencies will depart progressively from the mathematical harmonics. To get the necessary mass for the strings of an electric bass, wire is wound around a solid core wire.electric bass This allows the addition of mass without producing excessive stiffness.

6. PhysicsNTHU MFTai- 戴明鳳 Rotating saturn hexagon The hexagonal cloud feature at the north pole of Saturn is thought by most astronomers to be some sort of standing wave pattern. Saturn Rotatingsaturnhexagon.gifRotatingsaturnhexagon.gif from http://en.wikipedia.org/wiki/Standing_wave

7. PhysicsNTHU MFTai- 戴明鳳 原理 : 設一根均勻弦線，長 L, 質量 M, 單位長度質量密度  = M/L = m/  l 兩端固定繃緊, 張力 T 則弦振動時通過弦波 ( 橫波 ) 之波速 ( 以脈波為例 ) v  T   F net = 2·F sin  ~ 2F  (for small  angle ) = 2F [(  l/2)/R] =  v 2 /R = (   l)v 2 /R T  F =  v 2 目的 : 求弦振動 (string vibration) 時 之波速 、 波長及頻率

8. PhysicsNTHU MFTai- 戴明鳳 梅爾德裝置 (Melde Device) (1) 滑輪 (2) 砝碼 m (3) 弦線：一端固定於 (7) 直立 或橫擺音叉上 (4) 電磁鐵 (5) 白金接點 (6) 可變直流電源 (7) 直立或橫擺音叉：經可變 直流電源 (6) 及電磁鐵 (4) ， 可使白金接點 (5) 振動產生 特定頻率 f 令一端經滑輪 (1) 用砝碼 m(2) 使絃線固定繃緊, 張力 T = mg 則弦振動時之波速 v  mg    f  波長  測量波長 進行波 ( 以正弦波為例, 波方向 x 軸, 弦位移 y 軸 / 橫波 ) y(x,t) = y m sin[2  (x/ – ft)] = y m sin(kx –  t) 波向量 (wave vector): k = 2  角頻率 :  = 2  f

9. PhysicsNTHU MFTai- 戴明鳳 調整弦長 L 及張力 T (= mg), 使音叉端之入射波與反射端之反射 波重疊成駐波 (standing wave) 1. 結點 (node) ：位移 y = 0 點，音叉端及反射端固定, 位移亦為零 2. 反結點 (antinode) ： 位移最大 y = y m 點 3. 波長 : = 2L/n (n: 反結點數 ) 4. 音叉頻率 : f = v/ = (n/2L)(mg/  ) 1/2 f L m