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Chapter 14 - PowerPoint PPT Presentation


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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

Chapter 14

Superposition &

Standing waves

the principle of superposition
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.
interference of waves

Amplitude

Phase angle

Interference of Waves
  • Two waves traveling to the right
  • According to the principle of superposition, the resultant wave is:
interference of waves1
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

standing waves

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:
standing waves1
Standing Waves
  • In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.
standing waves in strings
Standing Waves in Strings

The wavelength of the nth mode of vibration

standing waves in strings2
Standing Waves in Strings
  • The fundamental frequency of vibration is adjusted by pressing and releasing the finger.
  • The length of string is changed!
a two dimensional standing wave on a disk
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.

beats interference in time

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: