Frequency Converter

Sample too slowly and frequencies don't disappear — they fold back and appear as signals that were never there. The Nyquist limit, aliasing, and why filters go first.

Every physical object has a natural frequency at which it vibrates most easily — and when an external force matches that frequency, energy accumulates until something gives. Here's why the Tacoma Narrows Bridge oscillated itself to destruction, why soldiers break step crossing bridges, how MRI machines exploit hydrogen resonance, and why wine glasses shatter at the right soprano note.

Equal temperament — the tuning system used by every modern piano and electronic tuner — is a mathematical compromise that makes all 12 keys equally slightly out of tune. Here's why pure integer-ratio intervals (like the 3:2 perfect fifth) can't fit in 12 notes without a gap called the Pythagorean comma, how equal temperament distributes that error evenly (making each fifth 0.745 Hz flat from pure), and why string players naturally drift toward pure intervals while pianists can't.

A "5.0 GHz" processor and a "3.5 GHz" processor — and the 3.5 GHz one can be faster for many real workloads, because GHz measures cycles per second, not work accomplished per cycle, and "work per cycle" (IPC) varies enormously between processor designs. Here's why GHz comparisons were more meaningful historically (within same-generation architectures), why core count adds a second dimension GHz doesn't capture, and why benchmarks matter far more than any single specification.

Concert A is 440 Hz because of a 1939 ISO standard. Here's how equal temperament maps notes to frequencies, why instruments at the same pitch sound different (harmonics and timbre), the Nyquist theorem that determines why CD audio samples at 44.1 kHz, and why different historical periods tuned differently.