The method you described with two accelerometers on two ends of a table, knocking on the table, is typically used to measure the speed of longitudinal waves. These longitudinal waves are also known as compression waves or pressure waves.
In a solid material like a table, when you knock on it, the disturbance generated at one end travels through the table as a series of compressions and rarefactions of the material. These compressions and rarefactions create a wave that propagates through the material, which is a longitudinal wave. The particles in the material vibrate parallel to the direction of wave propagation, causing compressions (where particles are closer together) and rarefactions (where particles are further apart).
Using two accelerometers placed at different distances on the table, the time it takes for the longitudinal wave to travel from one accelerometer to the other can be measured. From the time and the distance between the accelerometers, the speed of the longitudinal wave can be calculated.
It's worth noting that in a solid material, there can also be shear waves (transverse waves) and surface waves that propagate differently compared to longitudinal waves. However, the method with two accelerometers described in the video is primarily used to measure the speed of longitudinal waves in the material. To measure the speed of shear waves or surface waves, different experimental setups and methods are required.