Interference of Waves

Key Question

•What happens when 2 waves meet?•Animations:

▫http://phys23p.sl.psu.edu/phys_anim/waves/indexer_waves.html

▫http://www.earthguide.ucsd.edu/earthguide/diagrams/wave_interference/wave_interference.html

▫http://www.acs.psu.edu/drussell/demos/superposition/superposition.html

Wave Interference

•When pulses travel towards each other, the pulses interfere with each other for an instant and then continue travelling unaffected.

•All waves behave this way.

•Wave Interference – occurs when 2 or more waves act simultaneously on the same particles of a medium

Let’s Play with Waves• What will happen when a crest and a trough

meet?• What will happen when two crests meet?combinedwaveform

                                                      

wave 1

wave 2

Two waves in phase Two waves out of phase

Destructive Interference•The waves will

cancel out totally or partially

•Exactly out of phase – totally cancels – node.

Constructive Interference•Occurs when

waves build each other up, resulting in the particle having a larger amplitude

•Exactly in-phase: super-crest and super-trough

Resulting WavePrinciple of Superposition:

The displacement from equilibrium of each particle in a wave is a result of the energy transferred to that particle. The resultant displacement of two or more waves is the algebraic sum of individual displacements at one time, since the energy of the particle would be increased/decreased.

Example 1Add the two waves below to determine the resulting wave.

Example 2 (Stationary)Add the two waves below to determine the resulting wave.

Constructive or Destructive?

Homework1. Research noise cancelation headphones and give a one paragraph description of how they apply the principle of superposition. Include a diagram.2. Complete Interference of Waves Worksheet3. The principle of superposition can be used to explain why pulses are inverted when they reflect from the fixed end of a spring.a. What must the amplitude of a wave always be at the fixed end?b. If you consider the amplitude at the fixed end to be the result of the superposition of the incident and reflected waves, why does this necessarily imply that the reflected wave is inverted?c. Sketch a graph that shows the incident and reflected waves would appear at the fixed point.4. A washing machine sometimes bounces vigorously for a few moments at one or more of its spin cycle speeds. Explain the physics at work here.