Why can you hear someone talking around a corner — the low rumble of their voice, but not the crisp consonants? Sound bends around edges and through gaps, and long waves (bass) bend far while short waves (treble) fly straight and leave a sharp shadow. It’s why a subwoofer fills the house and the tweeter has to point at you. Slide from bass to treble and watch the shadow sharpen.
Diffraction — a wave spreading around an obstacle or through an aperture — scales with the ratio of wavelength λ to the size d of the edge/gap: the angular spread is ~λ/d. Sound wavelengths are large (a 100 Hz tone is λ≈3.4 m; a 5 kHz tone only ~7 cm), so low frequencies (λ ≥ the obstacle) bend generously into the geometric shadow while high frequencies (λ « the obstacle) cast a sharp shadow and beam straight. A fail-loud self-check throws unless the low-frequency spread is far larger than the high-frequency one. ◆ real wave acoustics, node-verified.
A λ/d spread estimate for a single edge/gap (the scaling, not a full Kirchhoff diffraction field); real rooms add reflections that also fill the shadow — the bass-bends-more, treble-beams-straight behaviour is the exact, defining scaling.