Sound Speed FormulaSpeed of Sound in AirSpeed of Sound in Various MediumFactors AffectingFAQs

Sound waves travel through a medium by alternately contracting and expanding the parts of the medium in which it travels.

We know that speed is calculated using the simple formula

**Speed = Distance/Time**

The speed of sound is defined as the distance travelled per unit time by any sound. In the next section let us learn to determine the speed of sound in various mediums.

## What is Speed of Sound?

The speed of sound is defined as the dynamic propagation of sound waves. This depends on the characteristics of the medium through which the propagation takes place. Speed of sound is used for describing the speed of sound waves in an elastic medium.

### Speed of Sound Formula

The formula for speed of sound is given with respect to gases. It is the square root of the product of the coefficient of adiabatic expansion and pressure of the gas divided by the density of the medium. The mathematical representation is given as:

\(v=\sqrt{\frac{\gamma P}{\rho }}\) |

Where,

- v is the speed of sound
- γ is the coefficient of adiabatic expansion
- P is the pressure of the gas
- ρ is the density of the medium

## Factors Affecting the Speed of Sound

There are two factors that affect the speed of sound:

- Density of the medium

For sound waves to travel, there is a requirement of medium and density of the medium is considered to be one of the factors on which the speed of sound depends. When the medium is dense, the molecules in the medium are closely packed which means that the sound travels faster. Therefore, the speed of sound increases as the density of the medium increases.

- Temperature of the medium

The temperature of the medium and the sound waves are directly proportional to each other. Therefore, as the temperature increases, the speed of sound increases.

## What is the Speed of Sound in Air?

The speed of sound is an essential parameter used in a variety of field in Physics. ** The speed of sound refers to the distance travelled per unit time by a sound wave propagating through a medium**. The speed of sound in air at 20

^{o}C is 343.2 m/s which translates to 1,236 km/h.

The speed of sound in gases is proportional to the square root of the absolute temperature (measured in Kelvin) but it is independent of the frequency of the sound wave or the pressure and the density of the medium. But none of the gases we find in real life are ideal gases and this causes the properties to slightly change.

### Example on Speed of Sound in Air

Question: The frequency of the middle C on the piano is 256 Hz. What will be the wavelength of the sound corresponding to the note of middle C if the speed of sound in air is assumed to be 345 m/s.

Answer: Let wavelength = λ

We know that, v = f.λ

Where, v = 345 m/s

And f = 256 Hz

Substituting the values in the equation, we get λ = 1.35 m.

## Speed of Sound in Solid, Liquid and Gases

Sound can travel through wood too! In fact, sound likes travelling through solid more. In the olden days, doctors used stethoscopes consisting of thin wooden rods with broadened ends and they worked exactly like our modern ones and performed just as well. How can sound travel through solids?

### Speed of Sound in Solid

Sound is nothing more than a disturbance which is propagated by the collisions between the particles; one molecule hitting the next and so forth. Solids are significantly denser than liquids or gases. This means that the molecules are closer to each other in solids than in liquids and in liquids than in gases. This closeness due to density means that they can collide very quickly. Effectively it takes less time for a molecule of a solid to bump into its neighbouring molecule. Due to this advantage, the speed of sound in a solid is larger than in a gas.

Speed of sound in solid is 6000 metres per second while the speed of sound in steel is equal to 5100 metres per second. Another interesting fact about the speed of the sound is that sound travels 35 times faster in diamonds than in the air.

### Speed of Sound in Liquid

Similarly, the density of a liquid is greater than the density of a gas. Therefore the distances between molecules are more in liquids than in solids but are less than in gases. Hence the speed of sound in liquids lies in between the speed of sound in solids and gases.

### Speed of Sound in Water

The speed of sound in water is more than that of the air. Or it can be said that the sound travels faster in water than in air. The speed of sound in water is 1480 metres per second. It is also interesting to know that the speed may vary between 1450 to 1498 meters per second in distilled water whereas the speed is 1531 metres per second in seawater when the temperature is between 20^{o}C to 25^{o}C.

### Speed of Sound in Gas

We should remember that the speed of sound is independent of the density of the medium when it enters a liquid or solid. Since gases expand to fill the given space, density is quite uniform irrespective of the type of gas. This clearly isn’t the case with solids and liquids.

### Speed of Sound in Vacuum

The speed of sound in a vacuum is zero meters per second, as there are no particles present in the vacuum. The sound waves travel in a medium when there are particles for the propagation of these sound waves. Since the vacuum is an empty space, there is no propagation of sound waves.

**Related Articles:**

### Table of Speed of Sound in Various Medium

The table below lists the speed of sound in various media. The proportional variation of speed with density is clearly visible here.

**The table shows the speed of sound in different materials**