13. Reflection of Sound: Echo and Reverberation

Like light, sound waves obey the laws of reflection when they strike a hard, large, rigid surface — the angle of incidence equals the angle of reflection, and the incident wave, the reflected wave, and the normal at the point of incidence all lie in the same plane. This reflective behaviour of sound gives rise to two important and frequently tested phenomena: echo and reverberation.

13.1 Echo

An echo is the repetition of a sound caused by the reflection of the original sound wave off a large, distant, hard surface (such as a cliff, a building, or a mountain), reaching the listener's ear as a distinctly separate, delayed sound after the original sound has already been heard. For an echo to be perceived as a distinct, separate sound (rather than blending with the original), the reflected sound must reach the ear at least 0.1 second (1/10th of a second) after the original sound — this is because the human ear retains (persists with) the sensation of any sound it hears for approximately 0.1 second, a property called the persistence of hearing; if the gap between the original sound and its reflection is shorter than this, the two blend together and no distinct echo is perceived.

Given that the speed of sound in air is approximately 340 m/s (at typical ambient temperature), and that the sound must travel to the reflecting surface and back (a total distance of twice the distance to the surface) within this minimum time gap of 0.1 second, the minimum distance between the source/listener and the reflecting surface required to hear a distinct echo can be calculated: minimum distance = (speed of sound × minimum time) / 2 = (340 × 0.1) / 2 = 17 metres. This value of 17 metres as the minimum distance required to hear an echo is one of the most frequently tested numerical facts in this chapter.

13.2 Reverberation

Reverberation refers to the persistence or prolongation of sound within an enclosed space (such as a hall, auditorium, or room) as a result of multiple, closely-spaced, and repeated reflections off the surrounding walls, ceiling, and floor, causing the sound to be perceived as continuing (decaying gradually) for some time even after the original source has stopped producing it. Unlike an echo, in which a single, clearly separated repetition of the sound is heard, reverberation consists of a great many overlapping reflections arriving in such rapid succession that they blend together into one continuous, gradually fading sound, rather than being perceived as distinct repeated echoes.

Excessive reverberation in a large hall or auditorium is undesirable because it causes successive spoken words or musical notes to overlap and blend into one another, making speech unintelligible and music muddled. However, some degree of reverberation is desirable — a room with essentially zero reverberation (acoustically 'dead') sounds unnaturally flat and lifeless. The design and control of reverberation and sound reflection/absorption within enclosed spaces to achieve optimal, clear sound quality is the domain of a specialised field called architectural acoustics. Auditoriums, concert halls, and cinema theatres are specifically designed with this in mind: their walls and ceilings are often given irregular, angled, or curved shapes to scatter and diffuse sound reflections evenly (avoiding the concentration of reflected sound into 'hot spots' or the creation of unwanted echoes), and sound-absorbing materials — such as thick curtains, carpets, perforated acoustic panels, and cushioned or fabric-upholstered seating — are used to absorb excess sound energy and control the reverberation time to an optimum value appropriate to the size and use of the hall.