1. Superposition Year 11 Physics

2. Some useful links showing animations of wave superposition. Here is three links to websites which provide good animations of wave superposition. http://www.kettering.edu/~drussell/Demos/superposition/superposition.html http://www.colorado.edu/physics/2000/applets/fourier.html http://id.mind.net/~zona/mstm/physics/waves/interference/waveInterference2/Wa veInterference2.htmlhttp://id.mind.net/~zona/mstm/physics/waves/interference/waveInterference2/Wa veInterference2.html

3. Two simple pulses The following is an animation of the superposition of two pulses approaching from different directions.

4. Two waves in same direction The following is an animation of the superposition of two sine waves of same frequency and amplitude but travelling at slightly different velocities.

5. Two waves in opposite direction – ‘Standing Waves’ The following is an animation of the superposition of two sine waves of same frequency and amplitude but travelling from opposite directions. Note how the resultant wave is a ‘Standing Wave’

6. Two waves of slightly different frequencies – ‘Beats’ The following is an animation of the superposition of two sine waves of slightly different frequencies travelling in the same direction. Note how the resultant wave is a ‘Beat’ with a much lower frequency

7. Captured Waveforms from a Yamaha Clavinova Digital Piano Sound waveform for a Grand piano

8. Captured Waveforms from a Yamaha Clavinova Digital Piano Sound waveform for Vibraphone – G above middle C Note how the waveform is more sinusoidal

9. Captured Waveforms from a Yamaha Clavinova Digital Piano Sound waveform for Vibraphone – two G’s above middle C Note how the waveform is more sinusoidal and is now twice the frequency of the previous slide

10. Superposition on the Digital Piano - The individual notes are played Firstly, here are waveforms for the note G above middle C and the next D above that note. Each note has been played separately. G above Middle C The next D above this G note

11. Superposition on the Digital Piano - Both notes played at the same time Here is the waveform for when the note G above middle C and the next D above that note are played at the same time. Note the complex resultant waveform produced.

12. Captured Waveforms from a Yamaha Clavinova Digital Piano - Decaying of waveform The following is an animation of a grand piano note been played showing the decay of the signal. (Mouse click in the middle of the image to start the animation)