﻿ All the formulas related to Sound Waves

# 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

$$v = \sqrt \frac{\gamma RT}{M}$$ $$= \sqrt \frac{1.4(8.314)T}{0.02895}$$ $$v = 20.05 \sqrt{T}$$