They are all measueres of sound waves. Amplitude is the term for the maximum difference in pressures between the peaks and troughs of a sound wave. Intensity is a measure of the energy content of a wave, and is proportional to amplitude squared. The decibel is an anthropic (based on human senses) measure of sound intensity, proportional to the logarithm of intensity.
The term that refers to the amount of energy a mechanical wave carries is "wave intensity." It is related to the amplitude of the wave and is determined by the square of the amplitude.
The decibel is a unit used to measure the intensity, or power, of a sound. It is a logarithmic unit that compares the power of a sound to a reference level. The decibel scale is commonly used to quantify sound levels and express changes in sound intensity.
The term for maximum displacement is the amplitude of the wave.
If you are referring to loudness of sound, then 'decibel' is a way of describing the loudness of sound. Rise in 10 decibel should mean rise of about 10 folds the initial level.
Intensity
The term that describes how loud a sound is is "volume." Volume is the measure of the intensity or amplitude of a sound, typically measured in decibels.
Amplitude refers to the amount by which something is displaced from the middle of its periodic motion. It can mean the maximum disturbance from the neutral position of a wave. It represents the intensity of a vibration, e.g. the loudness of a sound.
The practical usage term "volume" stands for the intensity of sound waves. Intensity in turn depends on the amplitude. Intensity is proportional to the square of the amplitude of the sound wave.
"Sound squared" is not a standard term in physics or acoustics. If referring to the concept of sound in a mathematical context, it could imply the square of a sound wave's amplitude, which relates to its intensity or power. In this sense, if you square the amplitude of a sound wave, you increase its perceived loudness, as intensity is proportional to the square of the amplitude. However, for specific applications, the term might need further context to provide a precise definition.
Sound waves are mechanical in nature. It means that it needs a material medium so essentially. As sound waves pass through the medium, the material does simple harmonic motion. Hence the energy is related to the amplitude of vibration. Energy is directly proportional to the square of the amplitude. Energy passing through the medium is derived in a formula as 2 pi2 m a2 f2. m- mass of the particle of the medium a-amplitude of vibration and f - the frequency of vibration. So the intensity is the term used to mean the energy of sound waves. It is defined as the energy per unit area crossing in one second.
Fringing vibrations.
The science term for high or low waves from the rest is called amplitude. Amplitude refers to the maximum extent of a vibration or oscillation, measured from the position of equilibrium.