Superposition of Waves

1. Superposition of Waves

2. Two important concepts that physicists study are Wave Motion Particle Motion • This semester will begin with the study of wave motion. • Particle motion will be studied later in the semester.

3. the material or substance that propagates a disturbance or wave • Your first experiment will show what happens when two waves are occupying the same region of a medium at the same time. • When this happens the waves interfere with each other and the combined waves take on a new shape. • You will learn how to determine that shape.

4. First let’s review the basic parameters of a transverse wave.

5. Wavelength Amplitude Transverse Wave Crest Baseline Trough

6. Next let’s look at the superposition of some simple combinations of two waves.

7. A crest of one wave is positioned with the crest of the other wave. The same can be said for troughs. • The first addition of waves that will be described involves two waves that are in phase. • This is referred to as constructive interference.

8. This represents the displacement by the white wave alone. This represents the displacement by the orange wave alone. Since they are both displacements on the same side of the baseline, they add together. Just repeat this step for several points along the waves.

9. A crest of one wave is positioned with a trough of the other wave. • The next addition of waves that will be described involves two waves that are out of phase. • This is referred to as destructive interference.

10. This represents the displacement by the white wave alone. This represents the displacement by the orange wave alone. Since the two displacements are on opposite sides of the baseline, the top one should be considered positive and the bottom one negative. Just add the positive and negatives together like this. Repeat this step for several points along the waves.

11. Finally we observe two waves that are partially in phase. • A different method of adding the waves will be demonstrated.

12. From the baseline measure to the “white” wave. Then add this to the “orange” wave. See animation. Continuing on with this process gives Note the white arrow would be zero in length here. Zero white arrows added to “orange” wave occur at these other locations. So zero added to the “orange” wave would give By overlaying the constructive interference curve from a previous slide you can tell that the curve of this slide is not fully constructive interference.

13. Interference Animation

14. For your experiment today you will be given two waves that are interfering with each other. • You will construct the resultant waveform by techniques similar to what you have just seen in this presentation. • There are also some calculations that you must complete. Important equations follow.

15. The frequency of a wave is the number of waves passing a stationary point per second. It is sometimes expressed as so many waves per second, so many cycles per second, or so many oscillations per seconds • The period of a wave is the time required for one vibration. It is also the time for a wave to travel one wavelength. • Period (T) and frequency (f) are inversely related.

16. In symbolic form or

17. For a wave, if the distance traveled is a wavelength (l), then the time to travel this distance is the period (T ). • Since the average speed is defined as a distance divided by time then

18. Remember that Therefore or

19. Thus if the experimenter can measure two of the three quantities v, l, and f, then the third can be calculated. • Please note that speed and velocity are two different descriptors of motion. You will learn more details about these descriptors in the second half of this course. What is important for you to understand at this point is that the symbol v being used in formulas throughout the manual and the PowerPoint shows represents speed, not velocity, although most of the time it also will represent the magnitude of the velocity.

20. Calculation Reminders How to manipulate the Hertz (Hz) unit. Just remember that one Hz is the same as 1/second (1/s). Example: What is the speed of a wave of frequency 500 Hz and wavelength of 2 meters.

21. Example Measurement An example of adding waves will now be done on an overhead projector or blackboard.