In quantum mechanics, the quasiparticle associated with a sound wave is called a phonon. The formula, E_Phonon=hv, is valid for the phonon where v is the frequency of the wave, h is plancks constant, and E is the energy of a single phonon. However, a typical sound wave is made of trillions of phonons.1. As the sound wave propagates away from the source, the energy is "thermally eaten". So, there is a gradual decrease in kinetic energy of the vibrating particles. Doesn't that lower the frequency of the sound wave? (i first considered from the classical energy point of view and then wondered if E=hv could be applied here? Please answer using both notions)
When a sound wave dissipates in classical physics, the amplitude of the wave decreases. When a sound wave dissipates in quantum mechanics, the phonon density corresponding to the wave decreases. The energy of each phonon doesn't usually change.
Let "n" be the number density of phonons corresponding to a wave of frequency v. The total energy density corresponding to the wave is:
where E_Total is the total energy density. Note that the total energy is the sum of the energies of the individual phonons.
There are two common misunderstanding regarding classical physics and quantum mechanics.
1) Some laymen think that classical mechanics doesn't allow discrete spacing of frequency.
-Classical physics allows the frequency of a standing wave to be "discretized".
-For instance, the modes of a plucked string with fixed endpoints has a quantized frequency even in classical physics.
2) Some laymen think that quantum mechanics is about quantization of frequency.
-In fact, quantum mechanics involves quantization of amplitude.
When a wave of a particular frequency loses or gains energy, it changes its amplitude. The frequency and wavelength do not have to change. The energy density of the wave is proportional to the square of the amplitude. The total energy of the wave has to change in discrete steps. However, this isn't because the energy of each particle changes in discrete steps. It means that the amplitude of the wave changes in discrete steps.
A change in amplitude for the wave corresponds to a change in number of the particles. The quantization of amplitude is inconsistent with classical physics. That is why Planck's theory raised eyebrows.
Planck hypothesized that the amplitude of the harmonic oscillator changed in steps. He did not imagine the quanta of energy as corresponding to changes in frequency of the harmonic oscillator. He assumed that the amplitude of each harmonic oscillator changed in steps that were proportional to the fundamental frequency of the harmonic oscillator.