The wave Equation and Superposition

7.3

The Wave Equation - Revision

TEXT: Page 240

Same Frequency Different wavelength?

An implication of the wave equation that is worth noting is that a source that has a specific frequency of vibration is able to produce waves of different wavelengths, depending upon the medium that carries the wave.

Q) What does this mean about the difference of the speed of sound in air and water?

A) If the same frequency is producing a longer wavelength this must mean that the wave is travelling further between pulses. A greater distance in the same time would mean a greater speed.

Example Problem

Waves meeting barriers• https://www.youtube.com/watch?v=6T82rOyytGU

• https://www.youtube.com/watch?v=YQHbRw_hyz4

Waves meeting barriersFixed End Free End

This means that the peak of the wave has moved half a wavelength from where it would have been. The peak is now where the trough was and the trough is now at the peak (The peak and trough are half a wavelength away from each other).

NOW LETS DO IT WITH THE SLINKY!!TIE BOB’S SHOE LACE TO ONE END OF THE SLINKY TO REPRESENT A FREE END

Superposition

• https://www.youtube.com/watch?v=BWraEDaVXZM

Superposition

Superposition – Constructive interference

Constructive interference occurs when two waves

meet that have particle displacements in the same

direction.

Superposition – Destructive interference

Destructive interference occurs when two wavesmeet that have particle displacements in oppositedirections.

Superposition – Both Types

Diffraction!

Diffraction!

We have seen how a wave can spread out from a point source, but waves are also capable of bending around obstacles or spreading out after they pass through a narrow gap. This bending of the direction of travel of a wave is called DIFFRACTION.

Summary