I'd like to introduce a method of displaying reflections in a room. This is called an ETC graph. It stands for Energy Time Curve. On the horizontal axis we have time, usually in milliseconds. On the vertical axis we have energy, you can think about this as sound level. A sound source in a room makes an impulse, a strong and very quick sound that contains all frequencies. In the old days before my time, it was often an air pistol puncturing a membrane. On the graph at zero time, we should see the largest spike. This represents the sudden sound of the pistol (or speaker!) reaching the microphone before any reflections. The sound to arrive first is always the direct sound, because it takes the shortest path directly from point A to point B. As we continue along the time axis we have nothing, then another spike. This is the first reflection to arrive, and it is lower in level than the direct sound because it lost some energy upon reflection. In a bare room, it will only have needed to reflect one time to travel from source to microphone. After that we see more and more reflections arriving. Some are low in level and some are not so low. This tells us that some needed to reflect a lot of times to arrive at the mic, and others didn't.
Image taken from RPG. Inc
The difference between a room showing reflections, and that with a diffuse sound field is down to the way the reflections arrive after the direct sound. Without the sound being diffused, we see no regular pattern to the reflections. Some are high in level and others are lower, although we do get a general trend for the average level and time gap to reduce as we progress in time. A diffuse sound field has a precise pattern to the way the reflections arrive. They start high in level, and get lower exponentially. The individual reflections are many, and the time gap between each is smaller in comparison to sparse non-diffuse reflections. Compare the above ETC with the one below and we can see the second ETC shows a smoother decline and more even spread of late arriving reflections. This is a more diffuse sound field.
This is important to the sound quality of a listening room because if the reflections decrease in level exponentially, and there are no unusual gaps in the time of arrival, we know the sound is evenly spread across the room. If we hear individual reflections arriving at our position after the direct sound then we are distracted from the true source of sound. When the reflections are spaced close together and smoothly reducing in level we don't dear them as a sound source, they are perceived simply as added spaciousness and don't tonally colour the sound.