Final answer:
Waves transfer energy through matter without permanent movement of the matter itself; sound requires a medium, light does not. The statement is true, as waves can transfer energy and momentum. Waves propagate faster in less dense mediums if their stiffness is the same.
Step-by-step explanation:
The statement that waves transfer energy through matter, where the matter remains essentially in place, is true. Waves, such as sound waves or light waves, can carry energy and momentum from one location to another. An important concept to understand is that this transfer does not involve a permanent movement of mass from one location to another; rather, the particles of the medium through which the wave travels may oscillate around their equilibrium positions, enabling the propagation of the wave.
For example, when we speak of mechanical waves such as sound, these require a medium like air, water, or solid matter to travel through. The molecules in these media will oscillate, but they do not travel with the wave itself and essentially stay put on average. On the other hand, electromagnetic waves such as light do not require a physical medium and can propagate through a vacuum.
Regarding the speed of wave propagation, it is generally true that waves propagate faster in a less dense medium if the stiffness (or rigidity) of the medium is the same. This is because the particles in a less dense medium can move more easily, facilitating the transfer of energy and momentum through the wave.
In summary, waves are disturbances that carry energy, but they do not carry matter along with them. This concept is captured in Big Idea 6 of the Advanced Placement (AP) Physics framework, which states that waves are mathematical models that can transfer energy and momentum without the permanent transfer of mass.