Lesson13 Interference
Lesson 13: Interference and Linear Superposition
Key Points:
• Understand what happens when two waves occupy the same space.
• Learn the two types of interference.
• Understand how this can be applied to practical uses.
Jan 9­12:44 PM
The Principle of Linear Superposition and Interference Phenomena There is a straightforward way to deal with situations in which two or more waves pass through the same place simultaneously. The diagrams at right show what happens when waves interfere with each other. Jan 9­12:44 PM
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Lesson13 Interference
The Principle of Linear Superposition and Interference Phenomena In the right diagram both pulses are “up” and in the left diagram one pulse is “up” the other is “down”. When the pulses merge, and the slinky assumes a shape that is the sum of the shapes of the individual pulses. Thus, when the two up pulses overlap completely, as in the left figure, the slinky has a pulse height that is twice the height of an individual pulse. Jan 9­12:44 PM
The Principle of Linear Superposition and Interference Phenomena Likewise, when the two “opposite” pulses overlap exactly, as in the right figure, they momentarily cancel, and the slinky appears straight. In either case, the two pulses move apart after overlapping, and the slinky once again conforms to the shape of the individual pulses. The adding together of individual pulses to form a resultant pulse is an example of the Principle of Linear Superposition. Jan 9­12:44 PM
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Lesson13 Interference
Principle of Linear Superposition When two or more waves are present simultaneously at the same place, the resultant wave is the sum of the individual waves. Jan 9­12:44 PM
Interference When two waves always meet condensation to condensation and rarefaction to rarefaction (or crest to crest and trough to trough), they are said to be exactly in phase and to exhibit constructive interference. Jan 9­12:44 PM
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Lesson13 Interference
Interference When two waves always meet condensation to rarefaction (or crest to trough), they are said to be exactly out of phase and to exhibit destructive interference. Jan 9­12:44 PM
Interference In general, the important issue is the difference in the distances traveled by each wave when overlapping. A difference that is an integer (1,2,3…) number of wavelengths gives constructive interference while half integer (1.5,2.5,3.5…) number of wavelengths gives destructive interference. Jan 9­12:44 PM
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Lesson13 Interference
E.g. Two loudspeakers, A and b, are separated by 3.20m. A listener is stationed at point C, which is 2.40m directly in front of speaker B. The triangle ABC is a right triangle. Both speakers are playing identical 214Hz tones, and the speed of sound is 343m/s. Does the listener hear a loud sound or no sound? 3.2m
2.4m
Using Pythagorean theorem (√(3.20)2 + (2.40)2 = 4.00m) to find the length of AC since BC is 2.40m the difference in distances traveled between the two waves is 1.60m. So the listener will here a loud sound if the wavelength of the sound is any factor of 1.60m and no sound if it is half a wavelength out of phase.
λ = v/f = (343m/s) / (214Hz) = 1.60m So the listener hears a loud sound. Jan 9­12:44 PM
Review Activities
• Read pages 411 – 413 In Pearson.
Jan 9­12:44 PM
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