Final answer:
The pulse given by the equation y = aeᵒx² represents a transverse and potentially a standing pulse as there is no mention of time governing its motion. Therefore, the pulse is transverse. option a.
Step-by-step explanation:
The pulse described by the equation y = aeᵒx² where 'a' and 'b' are constants, does not exhibit motion or propagation with time, thus it represents a transverse pulse that is not traveling.
A transverse pulse involves displacement of the medium (the rope, in this case) perpendicular to the direction of the pulse's travel. However, in this case, since time 't' is not mentioned in the equation, the pulse is not shown to travel or move with time and is possibly just a snapshot of the pulse at a certain moment, which aligns with a standing pulse.
The pulse of the form y = aeᵇx² is a transverse pulse. In a transverse pulse, the displacement of the medium is perpendicular to the direction of motion of the pulse. In the given equation, the exponent on x² indicates that the pulse moves in the horizontal direction. Therefore, the pulse is transverse. option a.