# Speed of Sound

on . Posted in Classical Mechanics

Speed of sound, abbreviated as a, is the velocity at which sound waves propagate through a medium.  It represents the rate at which disturbances in the pressure and density of the medium are transmitted as acoustic waves.  The speed of sound can vary depending on the properties of the medium through which it travels, such as temperature, humidity, and composition.  In general, the speed of sound increases with an increase in temperature and decreases with a decrease in temperature.

In dry air at sea level and at a temperature of around 20 degrees Celsius (68 degrees Fahrenheit), the speed of sound is approximately 343 meters per second (1,125 feet per second, 1,235 kilometers per hour, or 767 miles per hour).  This value is often rounded to 340 m/s for simplicity in calculations.  It's important to note that the speed of sound can vary in different media.  For example, in water, the speed of sound is about 1,484 meters per second (4,872 feet per second) at room temperature.  The speed of sound is affected by the molecular interactions and elasticity of the medium.  When a sound wave passes through a medium, the molecules or particles in the medium oscillate, transmitting the wave energy.  The speed of sound is determined by the density and compressibility of the medium.

The speed of sound has various practical implications in fields such as aviation, meteorology, and underwater acoustics.  For example, in aviation, knowledge of the speed of sound is crucial for determining aircraft performance, including issues related to supersonic flight and the formation of sonic booms.  It's important to note that the speed of sound may be affected by other factors, such as humidity and altitude, which can alter the properties of the medium through which the sound waves travel.  Thus, the actual speed of sound in a given situation may deviate slightly from the standard values mentioned

## Speed of Sound formula

$$\large{ a = \sqrt{ \frac{K }{\rho} } }$$     (Speed of Sound)

$$\large{ K = a^2 \; \rho }$$

$$\large{ \rho = \frac{ K }{ a^2 } }$$

### Solve for a

 bulk modulus, K density, ρ

### Solve for K

 speed of sound, a density, ρ

### Solve for ρ

 bulk modulus, K speed of sound, a

Symbol English Metric
$$\large{ a }$$ = speed of sound $$\large{\frac{ft}{sec}}$$  $$\large{\frac{m}{s}}$$
$$\large{ K }$$ = bulk modulus  $$\large{\frac{lbm}{in^2}}$$ $$\large{Pa}$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$

## Speed of Sound formula

$$\large{ a = \sqrt{ k \; \frac{ p }{\rho} } }$$
Symbol English Metric
$$\large{ a }$$ = speed of sound $$\large{\frac{ft}{sec}}$$  $$\large{\frac{m}{s}}$$
$$\large{ k }$$ = specific heat ratio $$\large{ dimensionless }$$
$$\large{ p }$$ = pressure  $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$

## Speed of Sound formula

$$\large{ a = \sqrt{ k\; R \;T_a } }$$
Symbol English Metric
$$\large{ a }$$ = speed of sound $$\large{\frac{ft}{sec}}$$  $$\large{\frac{m}{s}}$$
$$\large{ k }$$ = specific heat ratio $$\large{ dimensionless }$$
$$\large{ R }$$ = gas constant $$\large{\frac{ft-lbf}{lbm-R}}$$   $$\large{\frac{kJ}{kg-K}}$$
$$\large{ T_a }$$ = absolute temperature $$\large{F}$$ $$\large{K}$$

Tags: Speed