Audio Engineering

88 Chapter 3

3.5 Temperature-Dependent Velocity ............................................................................

The velocity of sound is temperature dependent. The approximate formula for calculating
velocity is

c49 459 4. °F (3.7)

where c is the velocity in feet per second (ft/s) and °F is the temperature in degrees
Fahrenheit.

For Celsius temperatures:

c20 6 273. °C (3.8)

where c is the velocity in meters per second (m/s) and °C is the temperature in degrees
Celsius.

Therefore at a normal room temperature of 72.5°F, we can calculate:

49 459 4..72 5 1130 ft/s.

3.6 The Effect of Altitude on the Velocity of Sound in Air ..........................................

The theoretical expression for the speed of sound, c , in an ideal gas (air, for example) is

c

P



γ

ρ

(3.9)

where c is the velocity in m/s, P is the ambient pressure, ρ is the gas density, and γ is the
ratio of the specifi c heat of the gas at a constant pressure to its heat at constant volume.

Consider the equation

PV RT (3.10)

where P is the ambient pressure, V is the volume, R is the gas constant, and T is the
absolute temperature.

Considering the defi nition of density ( ρ ), our fi rst equation can be rewritten as

c

RT

M



γ

(3.11)

where M is the molecular weight of the gas.