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Lesson 7: Reverberation and Echo (201912A)

Lesson 7

Reverberation & Echo

Did you ever wonder why sound in big halls decays longer than that in bedrooms? This phenomenon has something to do with the ability of sound to be reflected or diffused. In this lesson, we will discuss with you why and how the sound can have such a long decay.

Figure 1. Sound in concert halls decays longer than in bedrooms (Envato, bialasiewicz & Aleks_Sg)


Reverberation: What is it?

In the previous lesson, you have learned that sound in a room can be reflected, scattered, absorbed, diffracted, and resonated. Now you can imagine what happens when you generate sound in an enclosed space where some or all of the surfaces are reflective. The sound will be reflected multiple times. These recurring reflections can make sound energy decay longer. This is when you can hear a reverb/reverberation. Now, let’s learn more about this phenomenon.

What are the factors that determine
reverberation time?

When we learn about reverberation, one aspect that we need to take a look in room acoustics is reverberation time. According to ISO 3382-1:2009, the definition of reverberation time is the duration required for the sound in an enclosure to decrease by 60 dB after the source emission has stopped. For example, if we generate 110 dB sound in a room and it needs 5 seconds to drop to 50 dB, the room’s reverberation time is 5 seconds.

The math of reverberation time

This parameter can be calculated by the well-known Sabine equation, that was derived by Wallace C. Sabine. Don’t worry! We will not talk about how we obtain the formula here. What we only need to do right now is to see what variables involved in this equation. By understanding the equation, you will know what affects the duration of the reverberation time.

Reverberation time or often notated as RT depends on the volume of the room (V), the total absorption coefficient of its surfaces (αtot), and its total surface area (Stot).

Figure 2. Sabine equation

Sabine equation gives us a simple idea about how the dimension of a room can affect the reverberation time. A large room will have a bigger chance to have more reverb.

Reverberation time is also affected by the surface material. We know before that if the sound is generated in a room, it will be reflected when it hits any reflective surface. Now, what happens when every surface in the room is absorptive? The sound will all be absorbed, so the sound energy in the room will decrease so quickly. This phenomenon of sound absorption explains how the absorption coefficient in a room affects the reverberation time.

As explained in the previous lesson, the absorption coefficient defines how well a material can absorb sound energy. You know that it is so rare to find a room with only one type of material. That’s why in the Sabine equation, we call it the total absorption coefficient. It counts all the material absorption coefficients on the room surface with respect to its surface area. If you have n types of material, the absorption coefficient is further defined as follows.

Figure 3. The formula of total absorption coefficient

Here, αi and Si are respectively the absorption coefficient and surface area of i-th material.


Live rooms vs dead rooms

When we talk about acoustics in a concert hall, usually we talk about live and dead rooms. This subjective parameter refers to room reverberation time. A live room has a long reverberation time. Rooms for music performances–usually for performances without sound systems)–have this kind of subjective parameter. On the other hand, a dead room refers to a room with a short reverberation time. It can be encountered in a recording room. Usually, this kind of room uses some absorber materials so that the sound tends to be absorbed by the surface.

Dead room [RT(60) = 0.6 s]

Live room [RT(60) = 2.0 s]

Figure 4. The difference between live rooms and dead rooms (mcsquared.com)


Standard design for reverberation time

According to DIN 18041:2004, the recommended reverberation time of a room can be determined from the graph of reverberation time as shown in Figure 5. This graph can help us determine the target of our room acoustics design. The strategy to produce a certain reverberation time requires a lot of works to do. Acousticians and engineers usually use computer simulations to avoid excessive work to calculate the reverberation time of their proposed design.

Figure 5. Recommended reverberation time (DIN18041:2004)


Trivia: The longest reverberation
ever measured

There are so many infamous places that have a long reverberation time such as Taj Mahal and Gol Gumbaz in India, Hamilton Mausoleum in Scotland, and Tombo Emmanuelle in Oslo, Norway. If you want to experience such places by yourself, go to your nearest city cathedral. If it’s large enough, you may experience a long reverberation time.

Have you ever known the place with the longest reverberation time? In “The Sound Book: The Science of the Sonic Wonders of the World”, Trevor Cox, a UK acoustical engineer explains his discovery about a place that has the longest reverberation time ever measured. This place is Inchindown oil storage tank that was used to supply the naval anchorage in the Cromarty Firth during World War II. This tank is 240 meters long, 9 meters wide, and 13,5 meters high and could hold 25.5 million liters of fuel.

Figure 6. Inchindown oil storage tank (www.warhistoryonline.com)

By using a gunshot as the impulse sources, Trevor Cox discovered that the reverberation time at 125 Hz and mid-frequency was 112 seconds and 30 seconds respectively. And the average number for all frequencies is 75 seconds.


Echo: What is it?

Now what happens when you have a very big room, let’s say a huge concert hall or an indoor stadium? You may hear echoes. An echo happens when human ears can distinguish the difference between the original direct sound and the reflected sound. It means that the reflected sound should have a sufficient magnitude and delay.


Where do we find an echo?

Commonly, human ears can recognize a time delay of 0.1 s or more. By knowing the sound velocity in the air that is around 343 m/s at room temperature and atmospheric pressure, you can approximately calculate how far at least sound should travel to generate an echo. The calculation is simply 343 m/s x 0.1 s = 34.3 m ≈ 34 m. So, now you have a clue when you should worry that echo will ruin the room you design. If you have a room where the length between any parallel surfaces is at least 34 m / 2 = 17 m, you may need to consider an echo mitigation strategy.


How can we tackle echos?

Previously, we know that by applying a material with a high absorption coefficient, it can absorb the sound energy. This strategy can indeed avoid an echo present in a room. It may work for rooms with a short reverberation time, like an auditorium. Though, when you want to design a concert hall or another room that needs a relatively long reverberation time, you will definitely need another strategy. One of the common techniques is to apply a diffuser (diffusor).

Diffuser is a type of acoustic panel that has an ability to diffuse sound. Like any other acoustic material, each diffuser has a specific range of work frequencies. When sound hits a diffuser, the sound energy will be jumbled up into multiple reflected sounds. Each of these sounds will hit another surface so that the total of all reflections will manifest into a reverb. By applying this, you will no longer notice an echo. The magnitude of the energy the reflected sound carries is not high enough to be recognized as an echo.

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