How is Reverberation Affected in a Closed Room?

Have you ever been in a cave? It is a pretty interesting experience. Despite whether or not you have been in cave though, the one thing that everyone knows about caves is that they echo, and they echo a lot. Yell once, and your will hear your voice again and again as it slowly fades into the depths of the cave. It is a creepy occurrence in a cave, but echos happen almost everywhere, even though you may not be able to distinctly make them out. Why do these echos happen though? Most people probably have a rough idea of what is happening, but I want to go deeper and see what is happening on the invisible spectrum of sound waves. In this project, I will be analyzing how sound reverberation (echo) is affected by its surroundings in a closed room.

A Reflection on Sound

Before we go into how sound interacts with other things, we first need to review what sound is. In its most basic form, sound is energy that is transmitted in a wave form. The amplitude and frequency of that wave causes the attributes which we commonly refer to as loudness, which is self-explanatory, and frequency, which corresponds to pitch, respectively.

High vs Low amplitude and pitch

As a form of energy, sound waves have physical effects on things that they hit or are transferred through. A common example is head-rattling bass that is frequently heard in movies and music. Like those low bass frequencies, the other frequencies act in a similar manner, just not in the same way that bass may feel.

Wave Collisions

If you really think about what can happen when a sound wave impacts a surface, there are really only three things that can happen:

1.  It can be reflected off the surface. (Reflection)

2. Its energy can transfer into the object. (Absorption)

3. It can go through the surface. (Transmission/Refraction)

Examples of how sound interacts with a wall

In the context of a closed room, I am going to assume transmission loss to be minimal (since most walls are designed that way), so the main factors I will be considering are reflection and absorption.

Absorption

Absorption, quite simply, is the amount of sound energy that is absorbed into a surface upon a sound wave impacting it. There are two different types of material that absorb differently, solid and porous.

Solid materials simply absorb sound energy directly when it hits it. These generally do not absorb very much energy, since the sound waves are quicker to be reflected than transmit their energy into the material. In my analysis, solid material mostly include walls, ceilings, tile, and wood flooring.

Think of porous material as a sponge, except with the holes being very small. As the sound wave hits the surface, it wants to keep going in the same direction, so what happens is it winds its way into the tiny holes in the material. Inside the holes, the waves bounce around violently, and as they are colliding with the material they rapidly lose energy which is transmitted into the material. Depending on the material, it may absorb more or less amounts of energy. In my analysis, porous material is represented in things such as carpet, rugs, beds, drapes, etc.

Reflection

Reflection, as the name suggests, if the event of sound waves being reflected off of some surface that they come into contact with.

Reflection behaves very similar to light waves. If you have ever shone a concentrated beam of light, such as a laser pointer, on a mirror, you would notice that the way the laser pointer is reflected depends on the angle that the beam of light is hitting the mirror. Similarly, the way that a sound wave is reflected off of a surface depends on the angle of impact θ.

For our tests, the angles will be pretty uniform, since the sound waves will be bouncing off the sides of rectangular rooms. Therefore, I will not be doing any analysis directly related to the angle, but it is important to know how it works.

Every time a sound wave hits a wall, the energy in the sound wave that is reflected becomes smaller and smallern, as energy is also being lost as absorption and transmission. This is where volume comes into play. When you have a larger volume of a room, sound will take longer to travel between each wall (even though the speed of sound is fast, it is still a noticeable difference). Because the sound takes longer to hit each surface, the energy takes more time to die off, thus hypothetically giving a longer reverb time. In analysis, one of my goals is to see if that is really the case through the data that I collect.

Reverberation

To measure reverberation, I used a tool called ClapIR for iOS. What this tool does is it measures the amount of time it takes for frequencies to drop by 60 dB, which is the standard unit for which reverberation is measured in. In common terms though, it is the time it takes for a sound to fade out of hearing. Using this, I am able to take multiple trials, and take the average to analyze. Here are the graphs that were created from multiple trials.

Room 1, te

The graph is pretty easy to read. On the x-axis the different frequencies are clearly labeled, 0-20000Hz. On the y-axis, it shows the Reverb time (to drop 60 decibels) in seconds. The black line is what is important, as it is taking the average of all the data being collected.

For my analysis, I took 6 samples from two different rooms, a large bedroom (2304 Cu . ft), and a small bedroom (1232 Cu. ft). Each of these bedrooms are made of the same materials and are basically similar to each other aside from the fact that one is has a larger volume than the other. This is important because when I want to calculate the effect that volume [of the room] has on reverb, I will want to keep absorption(which is effected by the materials in a room) constant.

For each room, I will be taking 3 measurements of reverb:

  1. Bare room with no absorbing materials.
  2. Room with 1 queen mattress (~24 cu. ft) and 1 small area rug (35 sq. ft).
  3. Room with 1 queen mattress, 1 full mattress, and 1 small area rug.

When I say no absorbing materials, what I am saying is that I am removing as much porous material as possible from the room, which includes anything foam, cloth, etc. leaving the room filled with mostly wood furniture.

Calculating absorption is actually very hard. To do so accurately, it is required that you use a sound-proof room in your tests. For the purpose and scope of my experiment, I do not have the ability to use a sound proof room to test absorption of anything. The most I can know is that there is the least absorption in the first test, more in the second, and the most in the last. Therefore, because I do not know the actual quantitative measurement of absorption in the rooms, I will be analyzing my data qualitatively.

For specifics, see the data here.

To do measurements, I placed an iPad in the center of the room as well as I could, making sure to keep the microphone exposed. Then, after making sure it was as quiet as possible, I repeatedly clapped two blocks of wood together, making the sounds that app would use to calculate the reverberation of the rooms. The app produced both the graph of the reverberance and the avg reverberance of the room.

From the data I took, I constructed a table to put everything into perspective.

What does it all mean?

I think there are two trends that can be drawn from the data.

First, if we look at the relative absorption amount vs the avg reverb with volume of room constant, we notice that a larger amount of absorptive materials creates a lower amount of reverb in the room.

Second, If we compare the volume of the room with the avg reverb when the absorption is constant, the larger room seems to give a longer reverb time overall.

From the data that I have collected, it seems that the conclusions that can be drawn are as follows:

  • As the amount of absorption increases, the reverb decreases.
  • As the volume of the room increases, the reverb increases.

Final Thoughts

I think this experiment was a good introduction for me to sound waves and acoustics and how they work. In my research, there was a lot of information that I learned, but it was far too much to all put into my project. In all fairness, there were a couple factors in my experiments that I did not(and could not) include, although I did try to keep them constant throughout. In the end though, I came up with a solid analysis and I am interested in looking further into the topic.

Where to go from here

The possibilities of this project are endless. For starters, I could analyze how the combined effects of volume and absorption affect the reverb in a room. As well, if I had the necessary resources, I could actually measure quantitative absorption of object to really get a solid conclusion of how it affects reverb vs my qualitative conclusion in this project.

Resources

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