what is the material between 2900 kilometers and 5200 kilometers below earths surface inferred to be

That would be the outer core.

If I remember my geology lesson correctly, Earth's layers are from center to the top:

inner core
outer core
lower mantle
upper mantle
astenosphere
mantle
crust
lithosphere

lower mantle

To determine the material between certain depths below Earth's surface, scientists rely on various methods that provide indirect evidence or inferences about the composition. Here's an explanation of how this inference is made:

1. Seismic Studies: One of the primary sources of information about Earth's interior is through seismic waves generated by earthquakes or artificially generated sources. These waves travel through the Earth and provide valuable data about the composition and structure of different layers.

2. Seismic Wave Velocities: When seismic waves travel through different materials, their velocities change depending on the density, elasticity, and state of the material. By analyzing the travel times and velocities of seismic waves, scientists can make inferences about the properties of the Earth's interior.

3. Earthquake Data: Seismic waves generated by earthquakes travel along various paths through the Earth's interior. These waves reach different seismic stations at different times, depending on the path they took. Data from multiple seismic stations is collected and analyzed to create a network of seismic readings, known as seismograms.

4. Seismogram Interpretation: By analyzing the seismograms, scientists can identify various types of seismic waves, such as primary (P) waves and secondary (S) waves. P-waves are compressional waves that can travel through both solid and liquid materials, while S-waves are transverse waves that only propagate through solid materials.

5. Earth's Core: Based on the behavior of seismic waves, scientists have inferred Earth's core to be composed mainly of a solid inner core and a liquid outer core. The outer core is mostly liquid iron and nickel, while the inner core is believed to be solid due to high pressure.

6. Mantle: Between the core and the crust lies the mantle, which constitutes the majority of Earth's volume. Seismic studies have shown that the mantle consists of a solid upper mantle and a partially molten lower mantle known as the asthenosphere. The uppermost part of the mantle, known as the lithosphere, includes the rigid plates of Earth's crust.

Therefore, between approximately 2900 kilometers and 5200 kilometers below Earth's surface, the inferred material is the lower mantle and possibly part of the outer core. It is important to note that these inferences are based on current scientific understanding and are subject to ongoing research and refinement.