How Sound Travels in Everyday Life

The speed of sound is defined as the rate of change in pressure with respect to the density of a medium through which the sound is travelling. Sound is an acoustic wave of vibrations defined by the compressions and rarefractions of pressure within a medium. The medium through which sound travelled in the early universe was a plasma, however in the universe today it depends on what we define as the medium.

Another important variable in evaluating the speed of sound in a material is to consider the temperature changes. As an area of a medium is compressed its temperature is raised and as it decompresses the temperature lowers. We can model the process using an adiabatic variation as shown.

In this relation, P refers to the pressure, rho refers to the density, alpha refers to a constant and gamma refers to the adiabatic constant.

Furthermore the adiabatic variation above can be related with the speed of sound in a medium below. 

The equation for the speed of sound within a gas is shown below, with the same constants as defined previosuly.

Finally using the ideal gas law, this can be simplified down further to equation below in order to express the speed of sound in a gas where k is the Boltzmann constant , T is the temperature and m is the mass of each individual particle.

Studying this equation, it is favourable for a gas to be less dense, or to have less massive particles in order to have a higher sound speed. This is due to the fact that gas particles weakly interact between one another and the less dense a gas is the less obstacles there are to move in order to have a higher speed of sound. Less massive particles also take less energy to move and thus the faster the speed of sound is.

The opposite is true for solids. In a solid, the particles are packed together tighter than a gas, which means that particles interactions are stronger. As a sound wave travels through a solid, a more dense material is favourable due to particles being packed closer together. This means a molecule vibrated in a solid will pass on its energy to a neighbouring particle quicker and thus the vibrations from the acoustic wave will travel through quickly. 

If one also considers the intermolecular force in a solid material, as a sound wave displaces a molecule in a material, the tighter the particles are packed the stronger the counteracting intermoleculer force will be in order to place the molecule back to its original unperturbed position. This allows for an efficient process in order to have a molecule ready to oscillate again, and thus increasing the speed at which the waves travels.

Hearing Sound Waves

By studying the fundamental equation below, we can understand how a travelling sound wave would be hypothetically heard if the speed of propagation was increased. 

A propagating wave is described by the equation below.

How does Sound in the Early Universe Work?

As mentioned previously the early universe was extremely hot and dense, which meant the medium throughout the early universe was a hot plasma. As the universe expanded the plasma contained variations. These perturbations caused particles within the plasma to gravitationally attract each other. As more particles are attracted, these clumps of particles had s greater gravitational attraction and they would start to attract light. As light fell into this well the temperature inside these clumps would increase. The temperature changes would create pressure forces counteracting the gravitational forces. These counteracting forces produced oscillations known as Baryonic Acoustic Oscillations (BAO).  

The oscillations produced as a combination of gravitational and pressure forces within the plasma medium which counteract each other. These perturbations are comparable to sound waves and are referred to as baryonic acoustic oscillations (BAO) due to the fact that they oscillate the medium in a similar fashion to sound. These sound waves travel within the plasma with gravity and pressure forces counteracting each other like a spring compressing and releasing.

Seeing Imprint of Sound in the Universe