22 Jan 2022

# What is the Speed of Sound? – Means, Medium, Spread, and More

## Speed of Sound

The velocity of propagation of pressure waves in any medium. It adopts the name of the speed of sound, most easily perceptible phenomenon.

Because the propagation of a sound in a material is the most transparent, and of all the vibratory types.

The best-known value of the speed of sound is the one referred to the propagation of a wave in the air under standard conditions and corresponds to 342 m / s (about 1,230 km / h).

For propagation in other media there are highly variable values: 1,461 m / s (5,260 km / h) in water. 5,000 m / s (18,000 km / h) in steel and 30-70 m / s (100-150 km / h) on the rubber.

The velocity of propagation of pressure waves is of fundamental importance in the study of resonance phenomena in the collectors of reciprocating engines. It depends on the characteristics of the environment.

In the case of a gas, for example, the carbureted mixture. In the intake manifold or the gases burned in the exhaust manifold. Depends on their density and the pressure at which they are finding.

## Means, medium

We can define a medium as a set of oscillators capable of vibrating by the action of a force:

• When we speak of a medium, and unless something else is explicitly indicating, we will be referring to air. It is again due to practical reasons, insofar as philosophy is the most common medium in which the propagation of sound.
• Is carried out in communicative acts using acoustic systems between human beings, either through speech or music. For a sound wave to propagate in a medium, it must meet at least three fundamental conditions: be elastic, have mass and inertia.
• Sound waves do not propagate in a vacuum, but there are other waves, such as electromagnetic ones, that do.
• Air as a medium also has other relevant characteristics for the propagation of sound. Propagation is linear, which means that different sound waves (sounds) can propagate through the same space at the same time without affecting each other.
• It is a non-dispersive medium, so the waves propagate at the same speed regardless of their frequency or amplitude.
• It is also a homogeneous medium, so that sound spreads spherically, that is, in all directions, generating what is called a sound field.

• As we have already mentioned, an oscillating body sets the air molecules (from the environment) that surround it in motion. These, in turn, transmit this movement to neighbouring molecules and so on.
• Between the sound source (the oscillating body) and the receiver (the human being), we then have a transmission of energy but not a transfer of matter. It is not the air molecules that surround the oscillating body that make the eardrum move. But those that are next to it, which were set in motion as the wave propagated in the middle.
• The (small) (oscillatory) displacement suffered by the different air molecules generates areas where there is a higher concentration of molecules (higher density). Condensation areas and spots where there is a lower concentration.
• And also, molecules (lower viscosity), rarefaction areas. Those areas of higher or lower density generate an alternating variation in the static pressure of the air (the pressure of the air in the absence of sound). It is what is known as sound pressure.

## FIGURE 01:

• The distance between the bars represents the areas of higher or lower sound pressure.
• If the body that generates the oscillation performs a simple harmonic motion, the pressure variations in the air can be on behalf of utilizing a sine wave.
• On the contrary, if the body performs a complex movement.
• The sound pressure variations must be meaning using a waveform equal to the one resulting from the projection in time of the direction of the body.

## FIGURE 02:

Pressure Variations in the air (condensation and rarefaction) in the case of a simple harmonic motion.
The dots represent the air molecules:

As we said, in air, sound spreads spherically, that is, in all directions. We can imagine sound propagating as a sphere whose centre is the sound source and which is getting bigger and bigger:

Or, what is the same, that its radius is increasing every time?

• For convenience reasons, to study sound we can do it from one of these two points of view, sometimes as a growing sphere, or as a radius (eventually all radii) of it (rays).
• The distance that exists between two consecutive particles in the same phase situation is called the wavelength ( ). We can also define the wavelength as the distance that a wave travels in a period T.
• The wavelength is related to the frequency f (inverse of the period T) using the speed of propagation of sound (c), so that c = · f. Sound waves have wavelengths between about 2 cm and 20 m.
• We must not confuse the speed of propagation of the wave with the speed of movement of the particles.
• These perform a swift oscillatory activity, whose rate is different from the speed of propagation of the wave.
• The speed of sound in air is approximately 344 m / s at a temperature of 20º C, which is equivalent to about 1,200 km / h (1,238.4 km / h, to be precise). In other words, it takes about 3 s to travel 1 km. (As a possible reference, let’s remember that the speed of light is 300,000 km / s.)
• Sound travels at different speeds in media of varying density. In general, it propagates faster in liquids and solids than in gases (such as air).
• The speed of sound propagation is, for example, around 1,440 m / s in water and around 5,000 m / s in steel.

## Standing waves

So far we have talked about waves propagating in a medium, that is, travelling waves:

• Standing waves are the result of the interference of two equal travelling waves propagating in opposite directions. For example, a wave that arrives perpendicular to a wall and reflects on itself.
• The characteristic of standing waves is that points are generating (eventually lines or planes). In which the amplitude of oscillation is always zero (nodes). And others in which it is still maximum (antinodes our bellies). The distance between the two nodes will be half the wavelength of the standing wave ( / 2).
• Given a frequency that generates a standing wave, the multiples of that frequency (i.e. the harmonics) will also produce standing waves.
• The order of the harmonic will determine the number of nodes that are growing. For example, the first harmonic will generate one node, the second two, and so on.
• Standing waves are relevant in the operation of musical instruments (the strings, the columns of air enclosed in a tube). But also in the modal resonances (the resonance modes) of the rooms.