Phonon Energy Counts Mode Packets - Solid-State Physics: Lattices, Phonons, and Band Filling Step by Step

A toy phonon packet ledger cites the accepted mode. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Wave speed and wavelength give the mode frequency

Speed 16 meters per second over wavelength 8 meters gives frequency 2 hertz.

f=v/\lambda=16/8=2\ \mathrm{Hz}

Phonon packet energy is counted in the training model

Four packets with h equal to 3 joules per hertz and frequency 2 hertz carry 24 joules.

E=packets\cdot h f=4\cdot 3\cdot 2=24\ \mathrm{J}