Main Answer
When a wave pulse is sent down a lightweight rope that is tied to a very heavy rope at the boundary, the reflected wave will be inverted and the transmitted wave will also be inverted.The option C is correct.
Step-by-step explanation
When a wave pulse travels from a lightweight rope to a very heavy rope at their boundary, some of the energy is reflected back and some of it is transmitted forward. The behavior of this reflected and transmitted waves depends on the properties of the two ropes.
In this case, we have a lightweight rope (with low density) and a very heavy rope (with high density). When the wave pulse reaches the boundary, it encounters a sudden change in density, which causes some of the energy to be reflected back and some of it to be transmitted forward.
According to the principle of conservation of energy, the total energy of the reflected and transmitted waves must be equal to the energy of the original wave pulse.
However, since the densities of the two ropes are different, the speeds of propagation for the reflected and transmitted waves will also be different.
The speed of propagation for the reflected wave is equal to the speed of propagation in the lightweight rope. This is because there is no change in density as we move back into the lightweight rope.
The speed of propagation for the transmitted wave is equal to the speed of propagation in the heavy rope. This is because there is a sudden increase in density as we move into the heavy rope.Now, let's consider what happens to the shape of the wave pulse as it reflects and transmits across this boundary.
Since the speed of propagation for the reflected wave is less than that for the transmitted wave, we expect that there will be some delay between these two waves as they travel along their respective paths. In particular, we can show that:
The reflected wave will arrive at any given point before the transmitted wave does. This is because it travels a shorter distance before reaching that point.
The reflected wave will have a different shape than the original wave pulse. Specifically, it will be inverted (i.e., its positive and negative peaks will be reversed) due to its change in direction at the boundary.
The transmitted wave will also have a different shape than the original wave pulse. Specifically, it will also be inverted due to its change in direction at the boundary and its slower speed of propagation relative to that of the reflected wave.The option C is correct.