10 Waves

Lecture 22/5/13

Phase difference in time

Simulation (download here) to illustrate for transverse wave
  • phase difference between two displacement-time graph
  • phase difference of two points on a wave in terms of position difference and time difference

Simulation (access here or download here) to illustrate phase difference for longitudinal wave.


Simulation of propagation of circular wavefront from point source (download here)

Simulation of propagation of spherical wavefront from point source (download here)


Demonstration of polarization

Two polarizers simulation (access link here)

Three polarizers showing electric field (access link here)

Another view of three polarizers simulation (access link here)

Yet another three polarizer simulation (access link here)

Lecture notes fill-in-the-blanks

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Lecture 20/5/13


A wave can be described as a disturbance that travels through a medium from one location to another location. Waves can be considered to be an energy transport phenomenon because energy is transferred from one point to another some distance away. A progressive wave transports energy without transporting matter. There is no transfer of particles of the medium between the two points.

Waves as combination of particles in SHM

Connected pendula
Notice how the motion of the particles are connected.

Simulation of connected particles
Access to the simulation either through website or downloading here.

Notice that each particles are executing SHM in vertical direction but the wave profile is moving to the right.

Phase difference

Pendula in-phase
Oscillating bodies are in-phase when their stage of motions are identical:

  • When one reaches maximum displacement (right), the other also reaches displacement (right)
  • Both will reach the equlibrium position at the same instant and at the same direction for the velocity
  • When one reaches maximum displacement (left), the other also reaches displacement (left)

Pendula in antiphase

Pendula out-of-phase

Visualising Phase Difference in a wave

Different points/particles on a wave are at different stages of motion, depending on the position.

Mathematical derivation of wave equation and phase difference

Deriving wave equation and phase from Lee Tat Leong

Simulation of phase difference
Access to the sim either through website or downloading here.

The angle subtended in the circle is the phase difference.

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