Wave Speed

$v_{\text{mechanical}}\approx \sqrt{\frac{\text{restoring force}}{\text{resistive inertia}}}$

Transverse Waves

$v_{\text{string}}=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{TL}{m}}$

• $T$ is tension
• $\mu$ is linear mass density

Longitudinal Waves

v_{\text{sound in air}}=\sqrt{\frac{B}{\rho}}=331K^{\degree}\sqrt{\frac{T}{273K^{\degree}}}$$v_{\text{sound}}=\sqrt{\frac{B}{\rho}}=331K^{\degree}\sqrt{\frac{T}{273K^{\degree}}}

• $B$ is the bulk modulus
• $\rho$ is the volume mass density
• $T$ is the air temperature