Introduction:
Earthquakes are natural phenomena that occur when there is a sudden release of energy in the Earth's crust. This release of energy generates seismic waves, which can be classified into different types, including P-waves (primary waves) and S-waves (secondary waves). Both P-waves and S-waves contribute to the destructive potential of an earthquake, but one of them is generally considered more destructive than the other.

Destructiveness of P-waves:
P-waves are the fastest seismic waves and can travel through solids, liquids, and gases. They have a push-pull motion, similar to that of a slinky, and can cause the ground to move both horizontally and vertically. P-waves are responsible for the initial shaking felt during an earthquake and can cause structures to vibrate in their direction of travel.

However, P-waves are generally less destructive compared to S-waves due to a few reasons:

1. Amplitude: P-waves typically have smaller amplitudes compared to S-waves. The amplitude of a seismic wave determines the amount of ground movement and the potential for damage. Since P-waves have smaller amplitudes, they tend to cause less destruction to structures.

2. Material Interaction: P-waves can travel through different materials, including rocks and liquids, without significant loss of energy. This means that P-waves tend to pass through structures rather than interacting with them directly. As a result, they have less potential to cause damage to buildings and infrastructure.

3. Propagation: P-waves are able to propagate over long distances, but their energy dissipates more rapidly compared to S-waves. This means that the destructive potential of P-waves decreases with distance from the earthquake's epicenter.

Destructiveness of S-waves:
S-waves are the second-fastest seismic waves and can only travel through solids. They have a side-to-side motion, similar to the movement of a rope being shaken. S-waves cause the ground to move perpendicular to their direction of travel, which can lead to significant damage.

S-waves are generally more destructive compared to P-waves due to the following reasons:

1. Amplitude: S-waves typically have larger amplitudes compared to P-waves. This means that S-waves can cause more pronounced ground movement, resulting in greater damage to structures and infrastructure.

2. Material Interaction: S-waves interact more strongly with materials and structures compared to P-waves. When S-waves encounter a building, for example, they can produce strong shaking and induce seismic forces that can lead to structural failure.

3. Propagation: S-waves have a more limited propagation range compared to P-waves. However, their energy is generally sustained over longer distances, meaning that they can cause damage further away from the earthquake's epicenter.

Conclusion:
While both P-waves and S-waves contribute to the destructive potential of an earthquake, S-waves are generally considered more destructive. This is due to their larger amplitudes, stronger interaction with materials, and the potential for sustained energy propagation. However, it is important to note that the actual destructiveness of an earthquake depends on various factors, including the magnitude, depth, and proximity to populated areas.