surface area of the curved surface of a cylinder = 2π r h, where r is the radius and h is the height, every doubling of the radius results in a doubling of the surface area, thus the sound intensity halves with each doubling of distance from the line source. Since p1 = 1 and p2 = 4 for every distance doubled, this results in a sound pressure decrease of approximately 3 dB. In reality, dimensionless point sources and one-dimensional line sources cannot exist; however, calculations can be made based on these theoretical models for simplicity. Thus there is only a certain distance where a line source of a finite length will produce a sound pressure higher than an equally loud point source. Interference pattern is the term applied to the dispersion pattern of a line array. It means that when you stack a number of loudspeakers vertically, the vertical dispersion angle decreases because the individual drivers are out of phase with each other at listening positions off-axis in the vertical plane. The taller the stack is, the narrower the vertical dispersion will be and the higher the sensitivity will be on-axis. A vertical array of drivers will have the same horizontal polar pattern as a single driver. Other than the narrowing vertical coverage, the length of the array also plays a role in what wavelengths will be affected by this narrowing of dispersion. The longer the array, the lower frequency the pattern will control. At frequencies below 100 Hz (wavelength of 11.3 ft) the line array which is less than approximately 3 meter long will start to become omnidirectional, so the system will not conform to line array theory across all frequencies. Above about 400 Hz the driver cones themselves become directional, again violating the theory’s assumptions, and at high frequencies, many practical systems use directional waveguides whose behavior cannot be described using classical line array theory. In short, the geometry of real-world audio line arrays as used in public address systems can only be modeled approximately by line array theory, and only in the 100–400 Hz range. High frequencies Practical line array systems act as line sources only in the low- and mid- frequencies. For the high frequencies, some other method must be employed to attain directional characteristics that match those of the lows and mids. The most practical method for reinforcement systems is to use wave guides