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Decibel scale · sound intensity level
Decibel scale · sound intensity level
L=10·log₁₀(I/I₀) · I₀=10⁻¹² · +10dB=×10强度
L = 10·log₁₀(I / I₀), reference I₀ = 1×10⁻¹² W/m²
Inverse-square law · sound intensity vs distance
Inverse-square law · sound intensity vs distance
I=P/4πr² · 每加倍距离 −6dB · 球面波
I = P / (4πr²) for a point source · L = 10·log₁₀(I/I₀), I₀ = 1×10⁻¹² W/m²
Speed of sound in different media
Speed of sound in different media
气体 √(γRT/M) · 空气343/水1480/钢5000 · 温度依赖
gas: v = √(γRT/M) · air ≈ 331·√(T/273) · solids/liquids: v = √(B/ρ)
Beats · two nearby tones
Beats · two nearby tones
f_beat=|f₁−f₂| · 包络脉动 · 平均音高 · 调音
Two close frequencies superpose into a slow amplitude envelope you hear as beats
Harmonic series · timbre
Harmonic series · timbre
基频+整数倍 f_n=n·f₁ · 泛音谱 · 音色
Overtones at integer multiples of the fundamental set the tone colour
Vibrating string · Mersenne's law
Vibrating string · Mersenne's law
梅森 f=(1/2L)√(T/μ) · n 阶模式 · f∝1/L·√T
Length, tension and mass density set the pitch; the mode number sets the shape
Resonance tube · standing waves in an air column
Resonance tube · standing waves in an air column
开管 nv/2L 全谐波 · 闭管 (2n−1)v/4L 奇谐波 · 驻波
Open–open pipe f = n·v/2L (all harmonics) vs closed–open f = (2n−1)·v/4L (odd only)
Helmholtz resonator · the note of a blown bottle
Helmholtz resonator · the note of a blown bottle
f=(v/2π)√(A/VL) · 瓶口吹气 · 空气塞振动
f = (v/2π)·√(A / (V·L_eff)) — the air plug in the neck bouncing on the cavity spring
Acoustic impedance · reflection at a boundary
Acoustic impedance · reflection at a boundary
Z=ρv · R=((Z₂−Z₁)/(Z₂+Z₁))² · 空气↔水99.9% · 耦合剂
Z = ρ·v · R = ((Z₂−Z₁)/(Z₂+Z₁))² · T = 1 − R
Sonar ranging · d = v·t / 2
Sonar ranging · d = v·t / 2
回声 d=vt/2 · 往返减半 · 水下测距
A pulse travels to the target and echoes back — round-trip time covers twice the distance
Active noise cancellation · destructive interference
Active noise cancellation · destructive interference
反相相消 · 合成幅 2A·|cos(φ/2)| · 180°→0
An anti-noise wave 180° out of phase cancels the noise — the sum goes to zero
Reverberation time · Sabine RT60 = 0.161·V / (S·α)
Reverberation time · Sabine RT60 = 0.161·V / (S·α)
赛宾 RT60=0.161V/ΣαS · −60dB 衰减 · 音乐厅~2s
The time for sound to decay 60 dB — larger rooms ring longer, more absorption dries them out