In theory, it is possible to design a 3-dimensional sound chamber replica with a sound system and sensors to perform sound tests that could provide information related to the area of an integral. However, calculating the area of an integral solely based on sound tests would be a highly complex and challenging task.
To calculate the area of an integral, you typically need mathematical techniques such as integration. Integrals involve the accumulation of infinitesimally small elements over a given interval. While sound tests could potentially provide some information about the environment and the properties of the sound waves, directly deriving the area of an integral from sound measurements would be a non-trivial task.
Sound tests could potentially provide information about the acoustic properties of the chamber, such as the reverberation time, frequency response, or sound pressure level distribution. These measurements could indirectly relate to the geometry or size of the chamber. However, obtaining precise and accurate information about the area of an integral solely through sound tests would likely require sophisticated modeling, analysis, and calibration techniques specific to the setup.
In summary, while a 3-dimensional sound chamber replica with a sound system and sensors could provide valuable data about the acoustic properties of the chamber, directly calculating the area of an integral solely based on sound tests would be challenging and would likely require additional mathematical modeling and analysis.