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Interference of 2 Waves.

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Two loudspeakers are placed side by side a distance d=4.00m apart. A listener observes maximum constructive interference while standing in front of the loudspeakers, equidistant from both of them. The distance from the listener to the point halfway between the speakers is l=5.00m.

One of the loudspeakers is then moved directly away from the other. Once the speaker is moved a distance r=60cm from its original position, the listener, who is not moving, observes destructive interference for the first time.

The attached picture shows the situation described. The upper speaker is initially at the same distance from the listener as the other speaker. Then it is moved a distance r=60cm. The dashed outline represents its new position. (Note that the distance, r1, between the listener and the speaker has not moved, whereas, r2, the distance between the listener and the speaker has moved.)

Calculate r1 and r2 (to 4 significant figures)

r1 = _________________m
r2 = _________________ m

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The interference of two waves are examined. The observed destructive interference for the first time is analyzed.

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Wave Optics : Interference

Two spherical waves with the same amplitude, A, and wavelength, lamda, are spreading out from two point sources S1 and S2 along one side of a barrier. The two waves have the same phase at positions S1 and S2. The two waves are superimposed at a position P. If the two waves interfere constructively at P what is the relationship between the path length difference dx = d2 - d1 and the wavelength. If the two waves interfere destructively at P, what is the relationship between the path length difference and the wavelength.

3. What does it mean to say that two sources of waves are coherent, for instance, the waves in questions 2 above? If the sources in question 2 were two flashlights, would you observe interference at P? Explain.

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