Directivity is a measure of the directional characteristic of a sound source. It is often expressed as a Directivity Index in decibels, or as a dimensionless value of Q. This is an important aspect of a sound source, especially in a reverberant field. When a balloon is popped, it sends sound out in all directions equally (for all practical purposes), and this would represent a Q value of 1. A person talking has a Q value of approximately 2, which means that sound radiates in a hemispherical pattern (half a sphere). Directivity is important because it helps indicate how much sound will be directed towards a specific area compared to all the sound energy being generated by a source. If you have a limited amount of sound energy available (like that produced by the human voice), you can increase the distance that your voice will cover by increasing the directivity of your voice. You have probably experienced this calling to someone outdoors, when you cup your hands around your mouth to increase the directivity. What you are doing is "directing" more of the sound generated by your voice in the direction you need it to go. Someone talking through a megaphone may improve their voice's Q value to 15-20. You could think of this like a nozzle on your garden hose. Your garden hose will deliver a fixed amount of water, you can spray it in a mist to cover a wide area, or you can shoot it in a stream to a distant location, it's the same amount of water either way.
In a reverberant space, directivity plays another role. A low Q source, like a person talking, or a balloon popping will excite the reverberant field very uniformly. This limits the distance you can communicate before speech is masked by the reverberant sound. If you could increase the amount of sound that was directed towards your target, and at the same time reduce the amount of sound that went off in all directions to add to the reverberant field, you could increase the distance you could communicate. This is what increased directivity does for you. Unlike the outdoor case we described above, where the unused sound is lost forever, in a reverberant space the unused sound bounces around and adds to the background noise. A high directivity source, like a voice through a megaphone, can significantly increase the effective communication distance.
Loudspeakers have to be selected on the same basis for use in reverberant spaces. This is part of the sound system design process for us, we evaluate the reverberation time of the space, and determine what the directivity of the loudspeaker has to be to communicate over the distances required. It is possible to have reverberation times so long that it is impossible to select a directional enough loudspeaker to work effectively. The situation is complicated further if there are several loudspeakers involved. The loudspeakers that don't point towards you just contribute to the reverberant field you hear, without contributing to the useful sounds you hear. In very reverberant spaces, where one speaker may have worked, adding four or five speakers may prove to be unworkable. This is why directivity is a critical specification for difficult acoustical environments. Here's a discussion on Loudspeaker Directivity as a Design Issue.
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