Final answer:
The mathematical relationship is that Intensity equals Power divided by Area (Intensity = Power/Area), with intensity being directly proportional to power for a constant area. Therefore, the correct option is a) Intensity = Power/Area.
Step-by-step explanation:
The mathematical relationship between intensity, power, and area is as follows: Intensity = Power/Area. This formula explains that the intensity of a wave is directly proportional to the power passing through a given area. For a constant area, the relationship between the intensity of a sound wave and power is that the intensity is directly proportional to the power transmitted by the wave.
In our context, if we know the power and the area through which the power is being transmitted, we can calculate intensity using this relationship. Given certain parameters such as a power of 1.00 kilowatt and an area of 0.300 by 0.400 meters, we would use these values in our intensity equation to find the result.
The SI unit of intensity (I) is watts per square meter (W/m2). The intensity of a sound wave is also related to its amplitude squared, showing how changes in amplitude affect the energy and therefore intensity of the wave.
Power is the rate at which energy is transferred and is measured in Watts (W). Area refers to the cross-sectional area through which the wave is passing, and is measured in square meters (m²).
Therefore, the correct option is a) Intensity = Power/Area.