### Loudness and Phase

You do not perceive the loudness (also called volume) of sound in direct proportion to the power contained in the disturbance. Your ears and brain sense sound levels according to the logarithm of the actual intensity. Another variable is the phase with which waves arrive at your ears. Phase allows you to perceive the direction from which a sound is coming, and it also affects perceived sound volume.

#### The Decibel in Acoustics

You have already learned about decibels in terms of signal voltage, current, and power. Decibels are also used in acoustics, and in this application, they are considered in terms of relative power. If you change the volume control on a hi-fi set until you can just barely tell the difference, the increment is one decibel (1 dB). If you use the volume control to halve or double the actual acoustic-wave power coming from a set of speakers, you perceive a change of 3 dB.

For decibels to have meaning in acoustics, there must be a reference level against which everything is measured. Have you read that a vacuum cleaner produces 80 dB of sound? This is determined with respect to the threshold of hearing, which is the faintest sound that a person with good hearing can detect in a quiet room specially designed to have a minimum of background noise.

#### Phase in Acoustics

Even if there is only one sound source, acoustic waves reflect from the walls, ceiling, and floor of a room. In above figure, imagine the baffles as two walls and the ceiling in a room. As is the case with baffles, the three sound paths X, Y, and Z are likely to have different lengths, so the sound waves reflected from these surfaces will not arrive in the same phase at the listener’s ears. The direct path (D), a straight line from the speaker to the listener, is always the shortest path. In this situation, there are at least four different paths by which sound waves can propagate from the speaker to the listener. In some practical scenarios, there are dozens.

Suppose that, at a certain frequency, the acoustic waves for all four paths happen to arrive in exactly the same phase in the listener’s ears. Sounds at that frequency will be exaggerated in volume. The same phase coincidence might also occur at harmonics of this frequency. This is undesirable because it causes acoustic peaks, called antinodes, distorting the original sound. At certain other frequencies, the waves might mix in phase opposition. This produces acoustic nulls called nodes or dead zones. If the listener moves a few feet, the volume at any affected frequency will change. As if this isn’t bad enough, a new antinode or node might then present itself at another set of frequencies.

One of the biggest challenges in acoustical design is the avoidance of significant antinodes and nodes. In a home hi-fi system, this can be as simple as minimizing the extent to which sound waves reflect from the ceiling, the walls, the floor, and the furniture. Acoustical tile can be used on the ceiling, the walls can be papered or covered with cork tile, the floor can be carpeted, and the furniture can be upholstered with cloth. In large auditoriums and music halls, the problem becomes more complex because of the larger sound propagation distances involved, and also because of the fact that sound waves reflect from the bodies of the people in the audience!