A long, light string (Region I) is attached to a heavier string (Region II) at a knot that is fixed in space. A single triangular transverse pulse is traveling to the right along the light string toward the junction. The pulse has an upward displacement, an amplitude of 4.0 cm, and a width of 30 cm measured from leading to trailing edge.
The linear mass density of Region I is one–fourth that of Region II, while the tension is uniform and identical in both regions.
Assume the medium is ideal (no damping) and that the pulse shape does not change appreciably while moving through either region.
(a) Describe whether the reflected pulse in Region I will be inverted or non-inverted. Explain your reasoning in terms of relevant wave properties at the boundary.
(b) Compare the wavelength of the transmitted disturbance in Region II with the wavelength of the incident pulse in Region I. State which is longer and justify your answer qualitatively without using numerical calculations.
(c) The energy carried by a wave pulse is proportional to the square of its amplitude. Based on this fact and your answers above, explain qualitatively how the total mechanical energy of the system is distributed between the reflected and transmitted pulses immediately after the interaction with the boundary.