實驗內容 實驗 A：一維橫波弦振盪與駐波共振 實驗 B：金屬長條片的橫波振盪 實驗 C：環形駐波振盪與電子軌道運動 實驗 D：彈簧縱波振盪

Presentation on theme: "實驗內容 實驗 A：一維橫波弦振盪與駐波共振 實驗 B：金屬長條片的橫波振盪 實驗 C：環形駐波振盪與電子軌道運動 實驗 D：彈簧縱波振盪"— Presentation transcript:

1 Lab 7 One-dimensional Standing wave and two-dimensional Chladni pattern

2 實驗內容 實驗 A：一維橫波弦振盪與駐波共振 實驗 B：金屬長條片的橫波振盪 實驗 C：環形駐波振盪與電子軌道運動 實驗 D：彈簧縱波振盪
實驗 E：二維共振之克拉尼圖案 (Chladni pattern)

3 A：transverse waves on a string B：resonance of metal strip
Experiments A：transverse waves on a string B：resonance of metal strip C：resonances of a metal loop D：longitudinal waves on a spring E：two-dimensional vibration modes of plates (Chladni pattern)

4 youtube影片觀賞 (Physics Girl: Chladni pattern)

5 一維橫波弦振盪 Wave equation 𝜕 2 𝑦 𝜕 𝑥 2 = 𝜇 𝜏 𝜕 2 𝑦 𝜕 𝑡 2 Velocity 𝑣= 𝜏 𝜇 ,μ:線密度，𝜏:張力 nondispersive

6 Nondispersive medium and dispersive medium 非色散介質與色散介質
A dispersive medium is a medium in which waves of different frequencies travel at different velocities.[1] With electromagnetic radiation (e.g. light, radio waves), this occurs because the index of refraction of the medium is frequency dependent.

7 振動儀 mechanical wave driver
Sine wave generator

8 振動儀

9 正弦波產生器 Sine wave generator
0-800 Hz in 0.1 / 1 Hz step

10 實驗 A：一維橫波弦振盪與其駐波共振 梅爾德(Melde)弦振盪實驗

11 A：transverse waves on a string
Melde’s string vibration

12 弦振動 String vibration V：波速， T：張力， ：線密度

13 弦振動 String vibration V：wave velocity， T：tension， ：linear density of string

14 駐波 (standing wave)

15 Experimental Procedures
Carry out following measurements for 最細的弦 1. Arrange the set up shown in slide 9 or Try to observe the standing wave at three different frequencies. 3. Determine the wave velocity and compare with calculated value. 4. Repeat steps 2 and 3 for different tension. 5. 將振動儀轉90°（如圖），此時振動方向平行弦，重複步驟2-3。

16 實驗 B：金屬長條片的橫波振盪

17 B：resonances of metal strip

18 懸臂(樑) Cantilever Kieth Turvey, American Journal of Physics, 58, 483 (1990)

19 懸臂(樑) Cantilever dispersive
Kieth Turvey, American Journal of Physics, 58, 483 (1990)

20 Experimental procedures
Determine the fundamental resonance frequencies for all strips. Plot the resonance frequency vs. strip length.

21 實驗 C：環形駐波振盪與電子軌道運動

22 C：resonances of a metal loop

23 Bohr’s hydrogen atom 角動量量子化 pr = nh/2  energy of hydrogen energy level de Broglie wavelength  = h/p   = 2r/n

24 Reference D. Bloom and D. W. Bloom “Vibrating Wire Loop and the Bohr Model”, Physics Teacher 41, 292 (2003). m can be any odd number and represents the number of nodes in the oscillation of the wire loop

25 Experimental procedures
Determine the resonance frequencies for six different number of nodes. Plot the resonance frequency vs. m2 (m = number of nodes).

26 實驗 D：彈簧縱波振盪 𝑓 𝑛 = 𝑛 2 𝑘 𝑚 T = kL m = m/L v = L 𝑘 𝑚
𝑓 𝑛 = 𝑛 2 𝑘 𝑚 T = kL m = m/L v = L 𝑘 𝑚 C. Rutherford “A fresh look at longitudinal standing waves on a spring”, Physics Teacher 51, 22 (2013).

27 D: longitudinal wave on a spring
𝑓 𝑛 = 𝑛 2 𝑘 𝑚 T = kL m = m/L v = L 𝑘 𝑚 C. Rutherford “A fresh look at longitudinal standing waves on a spring”, Physics Teacher 51, 22 (2013).

28 Experimental Procedures
Measure the mass and force constant of the spring. Try to observe the standing waves at three different frequencies. Determine the velocity of longitudinal wave and compare with calculation. Repeat steps 2-3 for different stretched length.

29 實驗 E：二維共振之克拉尼圖案 (Chladni pattern)

30 Chladni pattern

31 Experimental Procedures
Try to find out the resonance frequencies for five Chladni patterns for two different plates.

32 Ernst Chladni ( ) Taken from Wikipedia

33 Pattern observed by Chladni
violin-shape plate

34 Square plate violin-shape plate