Editing Openai/671d5c99-22c0-8009-9bcd-f236b76abd3f (section)

===== 1. For Sound Waves (Mechanical Waves) =====

In a sound wave, energy is indeed proportional to both amplitude and frequency but in a more specific way. Here's how you could demonstrate this relationship:
* Wave Amplitude: The energy of a sound wave is proportional to the square of the amplitude (AAA), which represents the maximum displacement of particles in the medium.
* Frequency (fff): The frequency of a sound wave also plays a role since a higher frequency means that oscillations occur more frequently, transferring energy at a higher rate.
* Density and Volume: The energy in a sound wave depends on the properties of the medium (like density ρ\rhoρ and speed of sound vvv) and the volume of the wave.

====== Formula Derivation ======

The intensity III (power per unit area) of a sound wave is often expressed as:

I∝ρvf2A2I \propto \rho v f^2 A^2I∝ρvf2A2
And since energy depends on intensity and volume, you can infer that:

Energy∝ρvf2A2V\text{Energy} \propto \rho v f^2 A^2 VEnergy∝ρvf2A2V
where VVV is the volume.