Superposition. Principle of. Wave Interference:

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1 Wave Interference: When waves meet each other they interfere with each other. The principle of superposition tells us that the way they interfere is such that the amplitude of the resulting wave is the sum of the amplitudes of the two (or more) waves interfering. Principle of Superposition May 10 9:44 AM Apr 11 1:26 PM 1

2 Superposition example: Apr 29 1:00 PM Constructive Interference: when waves interfere in such a way that the resulting amplitude is greater than the amplitude of either of the original waves. Destructive Interference: when waves interfere in such a way that the resulting amplitude is less than the amplitude of either of the original waves. Constructive example: when two crests meet a supercrest is created. when two troughs meet a supertrough is created. In the ocean, this phenomena creates rogue waves which have been responsible for sinking ships. This phenomena also explains why it can be dangerous to get too close to waves pounding on the shore. Destructive example: when two waves meet and cancel each other out. May 10 10:12 AM 2

3 Beats and Beat Frequency: Sound waves like water waves will interfere with each other and cause different effects. One of these effects known as beats. Beats are variations in volume of a sound. They are created when two sound waves of very similar wavelength interfere with each other. Sound #1: freq. = 437Hz Combined waveform: Beat Frequency = 6 Hz Sound #2: freq. = 443 Hz Jun 10 11:38 AM Calculating Beat Frequency: Beat Frequency = f 2 f 1 Example: The tires on a car rounding a turn rotate at different speeds. If one tire is rotating at 600 rpm and the other is rotating at 660 rpm. What is the beat frequency heard? f1 = 600 rpm = 10 Hz f2 = 660 rpm = 11 Hz Beat frequency = 11 Hz 10 Hz = 1 Hz Jun 10 11:57 AM 3

4 Interference (revisited): During the development of physics one of the hotly discussed topics was the nature of light. Some properties of light, such as rectilinear propagation of light led scientists to believe that light consisted of particles while other properties, such as the fact that light bends around corners or through a slot led to a wave nature of light. One experiment that was considered a major development in the theory of light was performed by Thomas Young and was known as Young's double slit experiment. Here is an explanation: Jun 1 1:10 PM Young's Double Slit Experiment: In his experiment, Young shone light onto a screen through a mask that had two very narrow slits placed close together. If the light were to behave like a particle one would expect to see two bright spots on the screen behind just as if spray paint were sprayed on two such slits. If light behaved like a wave one would expect to see an interference pattern on the screen much like two waves interfere constructively and destructively when they pass through two openings. When the experiment was completed, Young observed an interference pattern. This gave the wave theory of light more support. Jun 2 12:50 PM 4

5 Jun 3 9:17 AM Check out this video: Try this applet: Jun 2 1:02 PM 5

6 Imagine two waves being generated on the surface of the water: Note: The lines represent crests of the wave Jun 2 1:13 PM Imagine the waves overlap and interfere with each other: Jun 2 1:13 PM 6

7 Areas where two crests or troughs meet you get constructive interference which forms supercrests and supertroughs. In the case of light this would create brighter light. Areas where crest meets trough would cause destructive interference which in the case of light would form dark areas. Supercrests are shown as blue dots. Cancelation is shown by green circles. Jun 2 1:13 PM Formulas for Youngs Double Slit Interference (for constructive Interference, ie bright regions) Using the angle from center: d = distance between slits Refer to: Fig p. 427 Using the displacement from center: nλ = d sin θ n nλ = d X n L θ n = angle from center Xn = displacement from center L = mask to screen distance n = order number (note: to find dark bands use (n - 1/2) instead of n) Jun 3 9:32 AM 7

8 n = 2 n = 1 n = 0 n = 1 n = 2 Jun 7 11:45 AM May 9 11:15 AM 8

9 Complete #s 92, 94, 96, 98 p May 8 1:53 PM May 22 11:32 AM 9

10 May 22 11:38 AM Diffraction Diffraction is the bending of a wave as it passes an object. An example of a water wave bending as it passes through an opening smaller than the wave length of the wave is shown: If the opening is wider than the wavelength there would be a flat area in the resulting wavefront. Jun 7 11:47 AM 10

11 When light passes through a very narrow single slit (narrower than the wavelength of the light) it diffracts and produces a pattern very similar to that of a double slit In this instance, note that the order number n shows the areas of destructive interference (ie dark areas, minima) The formulas are otherwise very similar: nλ = w sin θ n nλ = w X n L Xn = position of "n" th order w = width of slit (note: to find bright bands use (n + 1/2) instead of n) Jun 7 11:54 AM Complete #s 100, 102, 103, and 104 on p.441 Jun 7 1:52 PM 11

12 Interference Double Slit n=2 n=1 n=0 n=1 n=2 Diffraction single slit n=2 n=1 n=1 n=2 Jun 7 2:35 PM May 12 10:03 AM 12