Periodic Sound Waves: Pressure & Displacement Intervals

[Gear300]

Apparently, by what I read, the pressure intervals are 90 degrees out of phase with the displacement intervals for a sound wave. How is that so? When the medium is compressed, shouldn't the pressure be at a maximum and when at rarefactions, shouldn't the pressure be at a minimum?

 

[Gear300]

bump...
but seriously...if a particle of the wave was displaced inward and outward...its maximum displacement should be where the pressure is highest and lowest, shouldn't it?...why are the displacement and pressure equations 90 degrees out of phase?

 

[baba89]

Yes, this statement is correct. The pressure intervals and displacement intervals of a sound wave are indeed 90 degrees out of phase. This can be explained by the properties of sound waves and how they propagate through a medium.

When a sound wave travels through a medium, it causes the particles of the medium to vibrate back and forth. These vibrations create regions of high and low pressure, known as compressions and rarefactions, respectively. When a compression occurs, the particles are pushed closer together, resulting in an increase in pressure. Conversely, when a rarefaction occurs, the particles are spread further apart, resulting in a decrease in pressure.

Now, let's consider a simple sound wave traveling through a medium. As the wave propagates, it causes the particles of the medium to vibrate in a back and forth motion. At any given point in time, some particles will be in a state of compression while others will be in a state of rarefaction. This means that at any given point in time, there will be a region of high pressure and a region of low pressure.

However, as the sound wave continues to propagate, the particles will continue to vibrate back and forth, causing the regions of high and low pressure to move. This movement creates a phase difference between the pressure and displacement of the sound wave. In other words, as the particles are moving from a state of compression to a state of rarefaction, there will be a brief moment where the pressure is at a maximum and the displacement is at a minimum. This is why the pressure and displacement intervals of a sound wave are 90 degrees out of phase.

In summary, the 90 degree phase difference between the pressure and displacement intervals of a sound wave can be explained by the back and forth motion of particles in a medium as the wave propagates. This phenomenon is a fundamental property of sound waves and is crucial in understanding how they travel through a medium.