A concert hall’s acoustic field has billions of vibrational degrees of freedom.

Evidence

At the highest audible frequencies the wavelength is about 1 cm. Each such cube has three degrees of freedom to vibrate. Thus, a hall with dimensions 20 × 40 × 10 metres has about 3 · 2000 · 4000 · 1000 = 24, 000, 000, 000 degrees of freedom to vibrate! — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 298

The acoustic behaviour of real rooms, auditoria, and concert halls is very complex. This can be understood when estimating the possible number of degrees of freedom for vibration in the sound field. At the highest audible frequencies the wavelength is about 1 cm. Each such cube has three degrees of freedom to vibrate. Thus, a hall with dimensions 20 × 40 × 10 metres has about 3 · 2000 · 4000 · 1000 = 24, 000, 000, 000 degrees of freedom to vibrate! — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 298

Categorization

• CANDY: A vivid, concrete number — 24 billion degrees of freedom in one hall — that makes an abstract difficulty tangible and memorable.
• DEEPTHINKING: Reframes why room acoustics resist exact computation: the sheer dimensionality of the vibrating field, not any particular difficulty, is the fundamental barrier.
• corroborated: 2 independent passages support this claim — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 298