Which waves of energy travel through the Earth’s layers and are influenced by density, incompressibility, and rigidity?

Seismic waves are the correct choice because they are specifically generated by the movement of the Earth's tectonic plates and are used to study the Earth's internal structure. These waves travel through various layers of the Earth and their behavior is significantly influenced by the physical properties of those layers, such as density, incompressibility, and rigidity.

When seismic waves encounter different materials—like solid rock versus molten magma—they change speed and direction based on the properties of those materials. For example, P-waves (primary or compressional waves), which are a type of seismic wave, can travel through fluids and solids, while S-waves (secondary or shear waves) only travel through solids. This differentiation is entirely based on the density and rigidity of the materials in their path.

In contrast, sound waves are mechanical waves that require a medium to travel and are typically influenced by factors such as temperature and pressure within that medium, but not directly by the Earth's structural layers. Electromagnetic waves and radio waves are forms of energy that can travel through a vacuum and do not depend on the properties of the Earth's layers in the same way that seismic waves do. Therefore, seismic waves are uniquely positioned to provide insights into the Earth's composition and behavior.