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Using Calculus to Plan an Open-Air Concert

A concert is a mass entertainment event held indoors, at concert halls, or outdoors (open-air festivals). These two formats differ greatly from each other. However, the goal of both events remains the same – to allow the audience to enjoy the musical performance. Indoor halls are designed for the best acoustics of sound. They are often circular and let sound waves travel around the inside of the building, like an echo bouncing back and forth. This makes the audience feel like they are surrounded by sound. Such places already have outlined spots for mounting music equipment with the highest efficiency. Thus, thanks to the fact that the building is engineered exactly for the purpose of conserving the sound, concert holders are not obligated with extra calculations and planning. On the other hand, open-air concerts can range from small, acoustic gatherings at municipal parks, to large music festivals that take place over several days and feature a large number of different artists. Such concerts take great amounts of planning to make sure that the stage is visible and, more importantly, audible from the entire seating area.
In this paper, we investigate the physics of sound events of both formats and derive a basic formula for calculating the coverage of a sound system.