Mission WM5 Boundary Behavior of Waves

Getting your Trinity Audio player ready...

Hold down the T key for 3 seconds to activate the audio accessibility mode, at which point you can click the K key to pause and resume audio. Useful for the Check Your Understanding and See Answers.

Diagram 1 below shows a pulse traveling through a medium and approaching a boundary with a second medium. Diagram 2 shows the appearance of the media several seconds later. Comparing Diagrams 1 and 2 would lead one to believe that the ____-colored medium is the most dense medium.

The diagram shows a before and after snapshot for a pulse traveling from one rope towards the boundary with another rope. The incident pulse in the red-colored medium (left side) is shown in diagram 1. The reflected pulse in the red-colored medium (left side) and the transmitted pulse in the green-colored medium (right side) is shown in diagram 2. Diagram 2 shows that the reflected pulse has been inverted (see second Know the Law section) and that the transmitted pulse is both shorter and slower (has not traveled as far from the boundary in the same amount of time).

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).

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.