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The Echo Phenomenon

In order to determine the correct parameters for the computer simulation, the phenomenon of an acoustical echo must first be understood. An echo is a reflection of sound that arrives at the listener some discrete time after the production of the original sound. Sound is a mechanical wave that travels though a medium by transferring energy between the medium's particles. The echo phenomenon occurs when a sound is propagating through air and encounters a dense barrier, such as a large wall, where it changes direction and returns to its source.
The perception of sound only endures in a human's memory for about 0.1 seconds, therefore any sound that takes longer than 0.1 seconds to return to the listener is perceived as an echo. Sound travels in air at a speed of approximately 340 m/s, thus there will be an audible echo if the reflection barrier is greater than 17 meters away from the source. In the case that a large number of undistinguishable reflections arrive at a listener, the proper term is reverberation.

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Modeling an Echo

A delay can be modeled in digital signal processing using a delay line, a gain control, and a summer, as shown in Figure 1 below. The input signal takes two paths, one fed directly to the summer, and the second through the delay line and gain control (delay mix), which adds a specified amount of delay and attenuation.

Figure 1: Diagram of the basic delay unit, or an echo device.

The parameters that are relevant to the ECHO simulation are the value of the delay line in milliseconds and the delay mix value, which is the coefficient of attenuation as the signal propagates. Each module in the ECHO simulation consists of a basic delay unit and an algorithm that controls the rate at which the peak level of light intensity is reached. The delay portion of the simulation can then be simplified to a loop which sends the input signal through the basic delay unit the correct number of times, corresponding to two times the number of modules in the specific ECHO installation.

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Example Simulation Results

Each simulation only requires input of the site’s dimensions. The simulation program can then calculate a list of possible scaling parameters (including the optimal number and placement of modules), with the user determining which parameters are the most aesthetically pleasing.

Sample Scenario:
Distance of ECHO installation site: 100 Meters --> 10 modules, each 10 Meters apart (With the first module being 10 Meters from the source)

100m / (340m/s) = .3 seconds --> time required for propagation of whole distance = .6 s

Takes .03 seconds to get to first module
Module to Module delay time: 0.03 s

The time delay and number of modules is then input into the simulation and an animation displays how the propagation will look. The user then scales the time delay up until the visualization of the echo is perceived most clearly. For this simulation the program output indicates that the best time delay is 0.2 seconds between each module. Thus, the scaling factor for this simulation is (0.2/0.03) = 6.67. This means that the visual echo will actually be traveling 6.67 times slower than the actual acoustic wave would travel. The other parameters that must be determined are the rate at which the peak intensity level is reached, and the coefficient of signal attenuation for each module.

Mariano Mora -Composer- + Matt Stabile -EE- + Andres Burbano -Artist-