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Two identical point sources are generating waves with the same frequency and amplitude.  The two sources are in phase with each other, so the two sources generate wave crests at the same instant.  The wavelength of the waves is equal to the distance between the two sources.

Two identical point sources are generating waves with the same frequency and amplitude.  The two sources are in phase with each other, so the two sources generate wave crests at the same instant.  The wavelength of the waves is equal to the distance between the two sources.

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Two identical point sources are generating waves with the same frequency and amplitude.  The two sources are in phase with each other, so the two sources generate wave crests at the same instant.  The wavelength of the waves is equal to the distance between the two sources.

 

A.

List all the labeled points where the waves from the two sources constructively interfere.  If there are no such points, indicate that by stating "none".  Separate each letter with a space.  Hint: Determine the difference in the distance that each wave travels from the point sources.  For example the difference between the distance travelled to B = 1.5λ - 0.5λ.  Constructive interference occurs at ΔL=nλ.  Destructive occurs at ΔL=nλ/2.

 

B.

List all the labeled points where the waves from the two sources destructively interfere.  If there are no such points, indicate that by stating "none".  Separate each letter with a space.  Hint: Constructive occurs at ΔL=nλ.  Destructive occurs at L=ΔL=nλ/2.

The diagram above illustrates an interference pattern created by two point sources emitting waves in phase with each other. **Diagram Explanation:** - The horizontal grid represents the medium through which the waves are propagating. - The symbols A, B, C, D, and E mark specific points on the grid. - Points labeled with an "x" indicate points of destructive interference, where the crest of one wave coincides with the trough of another, resulting in cancellation. - Two circles labeled as "Point sources" represent the locations of the two coherent sources of waves. - The symbol λ (lambda) represents the wavelength of the waves emitted by the point sources. The point sources are equally spaced, and they generate a wave pattern that interferes constructively and destructively in the surrounding medium. The areas marked with "x" indicate positions where destructive interference occurs. This destructive interference happens due to the wave path difference being an odd multiple of half wavelengths, thereby leading to a zero resultant amplitude at these points. In the horizontal distance between two consecutive "x" points, the wavelength (λ) is indicated, showing the periodic nature of the wave interference pattern. The equally spaced grid allows for a clearer visualization of how the waves from the two point sources interact with one another, creating regions of constructive and destructive interference. This diagram is useful for educational purposes, demonstrating concepts of wave interference, path difference, and superposition of waves.
Transcribed Image Text:The diagram above illustrates an interference pattern created by two point sources emitting waves in phase with each other. **Diagram Explanation:** - The horizontal grid represents the medium through which the waves are propagating. - The symbols A, B, C, D, and E mark specific points on the grid. - Points labeled with an "x" indicate points of destructive interference, where the crest of one wave coincides with the trough of another, resulting in cancellation. - Two circles labeled as "Point sources" represent the locations of the two coherent sources of waves. - The symbol λ (lambda) represents the wavelength of the waves emitted by the point sources. The point sources are equally spaced, and they generate a wave pattern that interferes constructively and destructively in the surrounding medium. The areas marked with "x" indicate positions where destructive interference occurs. This destructive interference happens due to the wave path difference being an odd multiple of half wavelengths, thereby leading to a zero resultant amplitude at these points. In the horizontal distance between two consecutive "x" points, the wavelength (λ) is indicated, showing the periodic nature of the wave interference pattern. The equally spaced grid allows for a clearer visualization of how the waves from the two point sources interact with one another, creating regions of constructive and destructive interference. This diagram is useful for educational purposes, demonstrating concepts of wave interference, path difference, and superposition of waves.
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