# 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:

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

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)

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.

Sine wave generator

0-800 Hz in 0.1 / 1 Hz step

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

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。

B：resonances of metal strip

Kieth Turvey, American Journal of Physics, 58, 483 (1990)

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

C：resonances of a metal loop

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

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

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

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).

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).

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.

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

Ernst Chladni ( ) Taken from Wikipedia