# Why do early reflections arrive less frequently than later reflections?

I am reading Joshua Reiss's Audio effects: theory, implementation and application. He states

"Reverberation is also more than a simple delay device with feedback. With reverb the rate at which the reflections arrive will change over time, as opposed to just simulating reflections that have a fixed time interval between them. In reverberation, there is a set of reflections that occur shortly after the direct sound. These early reflections are related to the position of the source and listener in the room, as well as the room’s shape, size, and material composition. The later reflections arrive much more frequently, appear more randomly, usually decay exponentially, and are difficult to directly relate to the physical characteristics of the room. These late reflections give rise to diffuse reverberation. An example impulse response for a room is depicted in Figure 11.2. Each vertical line marks when the original sound is repeated, and the height of each of these lines is the amplitude of the sound at that time.

He shows the following plot:

However, I'm confused why the density of times "when the original sound is repeated" increases. Intuitively, it looks like the amplitudes decrease over time. I imagine this is because as the sounds reflect off the walls, they lose energy and so their amplitudes decrease. But you can see from Reiss's plot that it looks like the number of times when the original sound is repeated increases in density.

Why does the number of times when the original sound is repeated go up?

Early reflections are mostly due to a single bounce off of a boundary; late reflections are due to multiple bounces. They’ve traveled a longer distance to get back to you, hence the later time and lower amplitude. Why are there more of them? Because there are a lot more opportunities for a sound to bounce twice than once, and even more opportunities for three bounces, and so on.

Reflections are just reflections. The early ones arrive before the later ones simply because they generally have less reflective distance to travel. Additionally, the term 'early' generally refers to reflections before an arbitrary order and 'late' reflections refer to everything else (up to the end of time) - an order being defined by the number of surfaces the sound has reflected upon before returning to its source point.

So it follows that there are always going to be more late reflections than early reflections due to the difference in time constraints.