List of formulas related to Sound Waves
Sound Speed
V (m/s): sound speed in environment with temperature t (celsius)
$$ v = 331.4 + 0.61 \text{x} t $$Sound Intensity
E: sound energy (J), P: sound power (W), A: the surface area of a sphere (m2), t: time (s)
$$ I = \frac{E}{t.A} = \frac{P}{A} $$ $$ A = 4 \pi R^2 $$Sound Intensity Level
I0: the standard reference sound intensity
$$ L = log \frac{I}{I_o}(B) $$ $$ L = 10 log \frac{I}{I_o}(dB) $$ $$ I_o = 10^{-12}(W/m^2) $$ $$ |L_2 - L_1| = a(dB)$$ $$ => I_2 = 10^a I_1 $$The Doppler Effect
Vo: the relative speed of the observer; vs: the relative speed of the source; v: the sound speed in this medium; fs, fo: sound frequency of the source and observer
$$ f_O = f_s \frac{v \pm v_o}{v \mp v_o} $$Sound Speed In Gases
V: speed of sound (m/s), R: universal gas constant, T: absolute temperature (K), M:molecular mass of gas (kg/mol), γ: adiabatic constant
$$ v = \sqrt \frac{\gamma RT}{M} $$ $$ R = 8.314J/mol K $$Example in air
$$ v = \sqrt \frac{\gamma RT}{M} $$ $$ = \sqrt \frac{1.4(8.314)T}{0.02895} $$ $$ v = 20.05 \sqrt{T} $$