(1856) Standing waves and energy level diagrams part 1

Properties of Waves

• Wavelength is a defining property of waves.

  • Demonstrated with a slinky, illustrating how it can propagate waves.

Unconfined Slinky

• An unconfined slinky can allow any wavelength to propagate.

• Holding the slinky at one end allows waves to travel freely down to the other end.

Confined Slinky

• When both ends of the slinky are held, only certain wavelengths can propagate.

• The fundamental wavelength is the preferred oscillation pattern when confined, analogous to a musical tone in instruments.

Musical Connection

• Different musical notes result from confining strings at different lengths, which alter propagating wavelengths.

• Without confining wavelengths, music as we know it wouldn’t exist.

Overtones and Frequencies

• In addition to the fundamental wave, other wavelengths (overtones) can exist based on confinement.

  • The first overtone has half the wavelength of the fundamental, effectively doubling the frequency.

  • The second overtone requires further confinement, demonstrating the specific wavelengths that can propagate under such conditions.

Standing Waves

• Standing waves are created in confined environments; they have distinct properties:

  • Ends are confined.

  • Only specific frequencies/wavelengths can oscillate within boundaries.

• Visual representation of standing waves:

  • Fundamental wave: illustrated as a specific tone (first harmonic).

  • Overtones: shown as higher harmonics with increasing frequency.

Dimensions of Waves

• Waves can be confined in:

  • One dimension (1D): demonstrated with the slinky.

  • Two dimensions (2D): illustrated with animations of vibrating drum heads, showing fundamental and overtone patterns.

  • Three dimensions (3D): more complex, but shares the same principles of confinement and wavelengths.

Electrons as Waves

• Electrons also exhibit wave-like properties:

  • Unconfined electrons can propagate with varying wavelengths in space.

  • Wavelength relates to velocity (de Broglie equation).

• Confinement of Electrons:

  • Commonly confined within atoms due to attraction to the positively charged nucleus.

  • When confined, electrons behave like standing waves, exhibiting allowing only specific wavelengths/frequencies.

Energy Levels of Electrons

• Each allowed frequency corresponds to a specific energy level:

  • Discrete energy levels can be labeled (E1, E2, E3, E4).

  • Confining an electron results in quantized energy states.

Conclusion

• Only particular wavelengths exist for confined waves, relating to both musical instruments and the behavior of electrons in atoms. The lesson emphasizes the concept of confinement and its implications on wave properties.