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So, a function with a minus sign is a wave traveling from the left to the right , i.e., in the positive direction. C

So, a function with a minus sign is a wave traveling from the left to the right , i.e., in the positive direction. Conversely, a function with a plus sign is a wave traveling from the right to the left , i.e., in the negative direction.

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So, a function with a minus sign is a wave traveling from the left to the right , i.e., in the positive direction. C

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  1. So, a function with a minus sign is a wave traveling from the left to the right, i.e., in the positive direction. Conversely, a function with a plus sign is a wave traveling from the right to the left, i.e., in the negative direction.

  2. Superposition principle: read the text at the top of the Web page linked . In the fragment: ...is simply thesum... insert an extra word: ...is simply the algebraic sum… It’s important to stress that. Interference, in physics, is the superposition of two or more waves resulting in the creation of a new wave pattern. Interference may be constructive (the displacements in individual waves add up), or may be destructive (they cancel out). Look at the second animation from the top, showing two traveling waves of slightly different-s. At one moment the interference is constructive, a moment later it’s destructive, again constructive, and so on.

  3. Now, look at the third animation from the top, showing the formation of astanding wave. Such a wave is created by theinterference of two waves of the same , traveling in opposite directions. Note that there are fixed spots in which the interference is always destructive. Such points are called “nodes”. Also, note that there are regions in which the interference is always constructive. They are called “antinodes”. Note that the nodes and antinodes do not move – it’s why such a wave is called a “standing wave”. Other standing wave animations:A good animation; Yet another one.

  4. In another PPT presentation (click on this to see it) we derived the equation for the speed of a transwerse wave traveling on a tensioned string:

  5. Typical experimental setup: the vibrator excites a wave traveling to the right. The wave is “backreflected” at the other end. So, there are two waves traveling in oppo- site directions, giving rise to a standing wave. node node The two ends of the horizontal part are “fixed”, there must be nodes at these points. F = M ·g

  6. Possible states: no nodes in between, one node, two nodes, and so on, corresponding, respectively, to wavelengths: L

  7. From “Dr. Toms triangle”: f =v / 

  8. Sound waves: A longitudinal sound wave is a “train” of alternating compressions and rarefactions in air or other medium. Sound waves may propagate in gases, liquids and solids. In solids (and only in solids) transverse sound waves may exist (but this is another story).

  9. Sound waves can be thought of in two ways: • In terms of compressions and rarefactions, i.e., • of alternating areas of higher and lower density • (or higher and lower pressure, because air • pressure is proportional to its density). • Or in terms of displacement of the air molecules • from their equilibrium positions. • These two kinds of waves are phase-shifted relative • to each other by a quarter-wavelength. • This is explained in the next slide.

  10. Understanding the difference between the “pressure waves” and “displacement waves” becomes important in studies of standing sound waves in pipes. Sound pipes and standing sound waves are used in many types of musical instruments (organs, trumpets, flutes, saxophones, clarinets, trombones,….). There are two types of sound pipes, with one open end and two open ends. (sound pipes with two closed ends are of lesser interest from the viewpoint of musical instruments – why?)

  11. Picture courtesy to this Web page – worth seeing!

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