Final answer:
Amplitude and power are directly proportional, and so are intensity and power for a constant area. Amplitude is directly related to loudness but independent of wave's speed and frequency. Intensity is expressed as I = P/A.
Step-by-step explanation:
In physics, especially when discussing wave properties such as sound waves, the relationships between amplitude, power, and intensity are crucial to understand. In the context of your options, statement A is true: Amplitude and power are directly proportional. Specifically, the power of a wave is proportional to the square of the amplitude. When considering a constant area, the intensity (I) of a sound wave is directly proportional to the power (P). Thus, the more accurate description is d from the reference which states that intensity is directly proportional to the power transmitted by the wave.
The relationship between amplitude and loudness is another example of this proportionality; as the amplitude of a sound wave increases, the loudness experienced also increases. It is important to note that amplitude is independent of both the speed and frequency of the wave.
It's also relevant to understand that the intensity of a sound wave, which is proportional to the square of its amplitude, can be mathematically expressed in relation to power as I = P/A, where P is the power transmitted through an area A, and the SI unit for intensity is Watts per square meter (W/m²).