Doppler Effect

fm=fsv−vmv−vsf_m = f_s\frac{v-v_m}{v-v_s}

Supersonic Speed

sin⁡θ=vsoundv[planar/[plan]]=1Mα\sin\theta = \frac{v_{sound}}{v_{[planar/[plan]]}}=\frac{1}{M\alpha}

Compressibility coefficient

κ=−1ΔP⋅ΔVV\kappa = -\frac{1}{\Delta P}\cdot \frac{\Delta V}{V}

Sound Pressure

p=−1κ⋅∂s∂xp = - \frac{1}{\kappa} \cdot \frac{\partial s}{\partial x}
p=∓p0cos⁡[2π(tT±xλ)]p = \mp p_0 \cos \left[2\pi\left(\frac{t}{T} \pm \frac{x}{\lambda}\right)\right]

Pressure Amplitude

p0=2πs0κλ=Zs0ωp_0 = \frac{2\pi s_0}{\kappa \lambda} = Z s_0 \omega

Acoustic Impedance

Z=ρvZ = \rho v

Speed of Sound (Fluid and Gas)

v=1κρv = \frac{1}{\sqrt{\kappa\rho}}
v=cpRTcvMv = \sqrt{\frac{c_pRT}{c_v M}}

Speed of Sound (String and Rod)

v=Fμv = \sqrt{\frac{F}{\mu}}
v=Eρv = \sqrt{\frac{E}{\rho}}

Sound Intensity

I=Z2s02ω2I = \frac{Z}{2} s_0^2 \omega^2
I=p022ZI = \frac{p_0^2}{2Z}

Sound Intensity Level

LI=10lgII0L_I = 10 lg \frac{I}{I_0}
medI0=1,0⋅10−12 W/m2\textup{med$I_0 = 1,0 \cdot 10^{-12}\,W/m^2$}

Refraction and Transmittance of Sound

R≡IrefIin=(Z2−Z1Z2+Z1)2R \equiv \frac{I_ref}{I_in} = \left( \frac{Z_2-Z_1}{Z_2+Z_1} \right)^2
T≡ItrIin=1−RT \equiv \frac{I_tr}{I_in} = 1-R

Harmonics (Strings and Open Cylinders)

fm=m⋅f1      m=2,3,4,...f_m = m \cdot f_1 \,\,\,\,\,\, m = 2, 3, 4, ...

Harmonics (Half Open Cylinders)

fm=(2m−1)⋅f1      m=2,3,4,...f_m = (2m-1) \cdot f_1 \,\,\,\,\,\, m = 2, 3, 4, ...