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Chapter 14

Chapter 14. Superposition & Standing waves. The Principle of Superposition. If two or more traveling waves are moving through a medium, the resultant wave function at any point is the algebraic sum of the wave functions of individual waves.

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Chapter 14

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  1. Chapter 14 Superposition & Standing waves

  2. The Principle of Superposition • If two or more traveling waves are moving through a medium, the resultant wave function at any point is the algebraic sum of the wave functions of individual waves. • Two traveling waves can pass through each other without being destroyed or even altered.

  3. Amplitude Phase angle Interference of Waves • Two waves traveling to the right • According to the principle of superposition, the resultant wave is:

  4. Interference of Waves • Some source of disturbance; • A medium; • Some physical mechanism through which particles of the medium can influence one another. In phase f=0, constructive interference Out of phase f=p, destructive interference Other phase f=p/3, y falls to somewhere between the extremes

  5. The function of a standing wave Standing Waves • Two waves, one traveling to the right and one to the left • According to the principle of superposition, the resultant wave is:

  6. Standing Waves • In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.

  7. Standing Waves in Strings The wavelength of the nth mode of vibration

  8. Standing Waves in Strings

  9. Standing Waves in Strings • The fundamental frequency of vibration is adjusted by pressing and releasing the finger. • The length of string is changed!

  10. A two-dimensional standing wave on a disk the fundamental mode A higher harmonic standing wave on a disk with two nodal lines crossing at the center.

  11. Amplitude varies in time Beats: Interference in Time • The displacement that each wave produced at a fixed point • According to the principle of superposition, the resultant displacement:

  12. Beats: Interference in Time

  13. That is all for the semester! Thank you!

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