For the medium to remain undisturbed as two pulses pass the same point, they must have.

different amplitudes

To understand why the medium must have different amplitudes for two pulses to remain undisturbed, let's first discuss what happens when two pulses with the same amplitude pass through the same point in a medium.

When two pulses with the same amplitude pass through a point in a medium, they superpose or combine with each other. The resulting wave is obtained by adding the displacements of each individual wave at that point. If the amplitudes of both pulses are the same, the displacements will add up, resulting in a larger displacement at that point. This is known as constructive interference.

On the other hand, if the amplitudes of the two pulses are different, their displacements will not add up perfectly, and the resulting wave at that point will have a different amplitude. This is known as destructive interference.

For the medium to remain undisturbed, it means that the pulses should pass through the point without causing any change or disturbance in the medium. In other words, the pulses should cancel each other out completely at that point, resulting in no displacement or disturbance. This can only be achieved when the amplitudes of the pulses are different, causing destructive interference and resulting in the medium remaining undisturbed.

Therefore, for the medium to remain undisturbed as two pulses pass the same point, they must have different amplitudes.