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The diagram shows an incident pulse traveling from a more dense rope (colored blue and on the left) towards the boundary with a less dense rope (colored red and on the right). The answer choices show the reflected pulse and the transmitted pules. By careful inspection, you should be able to determine in which case the reflected pulse has been inverted or not inverted and in which case the transmitted pulse is traveling slower or faster and is shorter or longer. Use of the Know the Law sections and some good thinking will allow you to pick the proper answer choice.
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Wave Speed, Wavelength and Boundary Behavior:
When a wave or pulse traveling through a rope reaches a boundary with another rope, part of the incident pulse is reflected off the boundary and part of the incident pulse is transmitted across the boundary. The transmitted pulse is moving through a different rope than the incident pulse. Since the speed of a wave depends upon the properties of the rope, the speed of the transmitted pulse will be different than that of the incident pulse. The general rule for wave speed is that waves travel faster in the least dense rope (assuming all other variables are held constant). Since the wave speed is related to the wavelength by the wave equation, a change in wave speed will also result in a change in wavelength. Like wave speed, the wavelength is always greatest in the least dense rope (assuming all other variables are held constant).
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Inversion of the Reflected Pulse
When a transverse wave or pulse traveling through a rope reaches a boundary with another rope, part of the wave or pulse is reflected and travels back through the original rope. The reflected part has the same wavelength, wave speed and frequency as the incident wave or pulse. However, the wave or pulse can become inverted (or flipped) if the end of the rope is attached to a more dense rope. Such a boundary causes any upward-displaced incident pulse to reflect as a downward-displaced reflected pulse. If the end of the rope is attached to a less dense rope at the boundary, then the reflected pulse will not be inverted.
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