2D Wave Interference

Jerry Liu 27275149

What is a 2D wave2D wave propagates in a plane, looks like ocean wave. The black region indicates large positive displacement and you can imagine it comes our of the screen.

If you observe the 2D wave on the same plane, you will see a 1D wave. In which the crest coincidence with the black line.

Interference

• Like 1D waves, 2D waves can interfere with each other, at a given time t0, you get the combined wave by adding the displacement of each wave together.

• Constructive wave forms where the black line (maximum positive displacement) meet with each other of each wave. The amplitude can be doubled.

• Destructive wave forms where the white region between the adjacent black lines meet with the black line of another wave. The largest positive and negative displacement meet with each other so that there is no particle displacement at all. The amplitude becomes zero.

interference

Constructive interferenceDestructive

interference

Problem

• Suppose you are the captain and your crew feel seriously seasick. By observing you figure out the water wave is a combined wave of two identical waves that only differs in direction, which way are you going to choose to minimize the shaking of the boat.

Choose the best route

B

A

C

D

YOU ARE HERE

Solution

• Route A will lead to a even worse situation, you can see that the crests and troughs reinforce each other, which create a larger vertical displacement.

• Route B will minimize the displace as you can see the crests of one wave always encounter the troughs of the other wave. Therefore the vertical displacement cancel out each other.

• For route C and D, the crests and troughs only sometimes cancel each other, but not always, so you can still feel the vibrations in the boat.

Further analysis

• Although you can figure out a route to minimize the effects of ocean waves in the question, but that is not useful in the real world.

• Firstly, the real ocean waves are always combined with much more complicated waves in comparison with the simple situation in the question. Therefore its hard to figure out a pattern for it.

• Secondly, whether you can choose the best route is depend on the wave length. For example, if the wavelength is 20 meters and your boat is 3 meters wide, it is possible to avoid the highest crests. However, if the wavelength is 50cm and you try to move your 3m boat a few cm to reach the best route, its obviously meaningless.

Conclusion

• Learning about 2D waves are very useful for learning 3D waves which are most common in our real world.

• The boat question is not a real world problem but a useful tool for your understand of 2D waves from a 2D wave picture.

• Thanks for watching.