Lesson 6

Behaviors of Sound in Rooms

To create high sound quality for music venues or speech listening rooms, we need to learn the science behind sound behaviors.

Some behaviors can improve or degrade sound quality inside a room. It depends on how you control those behaviors so that the sound waves can act the way you want.

When a sound wave propagates in a closed space and strikes one of the surfaces, it may undergo one or more of the following behaviors: (1) reflection, (2) absorption, (3) diffusion, (4) diffraction, and (5) resonance. Here, we will talk about all of those.

Reflection

When a sound wave strikes a surface, we can confidently say that some of the energy will bounce back in a different direction.

If you ever learn physics of sound in middle school, you may still remember that the reflected sound will have the same angle as the incident sound. Let’s see the illustration below to help you imagine how the sound bounces after it hits a surface.

Figure 1. Sound reflection

Draw a line perpendicular to the surface that starts from the point on which the sound wave is incident. This line is called the normal line. The angle between the direction of the incident sound wave and the normal line is then what we define as the incidence angle. The same applies to the reflection angle. For reflection in a flat surface, the reflection angle equals to the incidence angle.

However, in the real world, we may find that all reflections do not always seem to behave that way. If you observe how the sound hits a rough surface, you may discover that there are many reflected sounds and each of them goes in a different direction. Why does it happen?

Diffusion

When a sound wave strikes a rough or irregular surface, it actually follows the physics of reflection as we have discussed above—the sound wave will bounce back at the same angle as its incident wave. In this case, the incident sound hits many different surfaces; each of them has a distinct normal line. Thus, the reflection angle will vary according to which surface the incident sound hits. In results, the reflected sound is scattered at many angles. We call this phenomenon as acoustic diffusion.

Please don’t be confused when you encounter specular reflection and diffuse reflection in other articles or books. Those terms are synonymous with reflection and diffusion, respectively.

Figure 2. Sound diffusion

The sound energy that is reflected at angles other than the incident angle is called as scattered energy. In diffusion, there is a lot of scattered sound energy since the reflection will be spread into all directions. Some materials will have different scattered sound energy. It is based on their structure.

According to ISO 17497-1:2004, the scattering coefficient is the value calculated by one minus the ratio of the specular reflected acoustic energy to the total reflected acoustic energy.

This value ranges from 0 to 1, where 0 means a fully specular reflecting surface and 1 means a fully scattering surface. The scattering coefficient describes the degree of scattering due to the roughness or irregularity of a surface. It is used to measure the amount of sound scattered away from the specular reflection direction.

Absorption

Did you notice that when we discuss reflection above, we say that some of the energy will be reflected? Why only some of it? Because some of the other energy will be absorbed by the material. Now we will talk about absorption and the essential parameter associated with it, sound absorption coefficient.

Figure 3. Sound absorption

The sound absorption coefficient (α) is the ratio of the absorbed sound energy to the incident sound energy. The sound absorption coefficient of material ranges from 0 (absorptive) to 1 (reflective), and it varies with frequency. It can be measured using the room method according to American standard ASTM C 423 or international standard ISO 354. As α varies with frequency, it won’t be straightforward to be understood by common people. So we usually use a single number rate called NRC to simplify the term of α.

Noise reduction coefficient (NRC) is a single number that also ranges from 0 to 1 and is used to represent the percentage of sound energy absorbed by the surface. It can be a parameter to determine the effectiveness of sound-absorbing materials. The NRC number is the average of measurements of sound absorption coefficients at 125 Hz, 500 Hz, 1000 Hz, and 2000 Hz and rounded to the nearest multiple of 0.05. 

When the NRC of material is 1, it means that the material will absorb the sound energy entirely at 125 Hz, 500 Hz, 1000 Hz, and 2000 Hz. Now you may have got the idea that if two different materials have the same NRC rate, it does not always mean that both will have the same performance.

Diffraction

Did you ever realize you can hear a sound that goes through a small hole even though you are not directly in front of that opening? Did you also ever realize that you can still hear music from the stage even when you are behind a large post? The ability of sound waves to spread out after it escapes a small opening and to bend when after it hits an obstacle is defined as diffraction.

Diffraction depends on wavelength. The bigger the wavelength, the more the sound wave to bend or to spread out. If you want to know the relationship between the wavelength and frequency, see the formula below.

Figure 4. The relationship between wavelength and frequency

From this formula, we can conclude that diffraction is more dominant in the lower frequency because it has the bigger wavelength.

Figure 5. Low-frequency sound spreads out more than high-frequency sound with the same opening

Figure 6. Low-frequency sound bends more than high-frequency sound with the same obstacle

Resonance

In regard to sound behaviors, there is a significant difference between small rooms and large rooms. In a small room, like a listening room and recording studio, you may notice that the loudness of low-frequency sound is not distributed evenly across the room. This problem happens when you experience an acoustic resonance.

Acoustic resonance is a phenomenon in which sound waves have a frequency that matches one of the natural frequencies of the room. When it happens, the sound energy will create standing waves at these natural frequencies. It means that these sound waves do not travel. Therefore, the nodes and antinodes result in the uneven distribution of sound at natural frequencies.

The natural frequencies of an ideal reflective room can be derived with the following formula.

Figure 7. Natural frequency equation

Let’s take a look at the example in Figure 8 below. For simplicity, we only focus on the resonance that happens between two rigid walls in a rectangular room. Here, we see it from above. In this room the sound resonates as it maches the 2nd harmonic natural frequency of the room.

Figure 8. Resonance affects sound pressure distribution in a room

In this example, you can see that the sound pressure at point A and C is of the highest magnitude, while at point B, the pressure is zero. If you are at point A or C, you will hear the sound louder compared to that at point B. 

A group of resonances that present in a room generated by a sound source such as a loudspeaker or acoustic music instrument creates room modes.

Room modes affect the low- to mid-frequency response of live music or music reproduction in rooms. Imagine how bad it will be if all these resonances come together. If not treated, they will degrade sound quality.