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Wize University Physics Textbook (Master) > Sound & Hearing

Sound Waves Patterns

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Sound Waves Patterns


Sound waves are longitudinal mechanical waves for which the direction of motion of particles in the medium is along the direction of the wave propagation.

Sound waves in air are produced by compression and rarefaction of air molecules. As a result of oscillation in the density of the air molecules, the pressure of air molecules also oscillates. So, a sound wave pattern can be shown by either displacement curve of air molecules or by pressure oscillation.

To understand this better, imagine an air pipe with an oscillating piston at one end of this air pipe. Let's consider the other end to be closed. When the piston moves, it will generates a wave of compression and rarefaction of air molecules along the pipe.

Note :

  • Air molecules right beside the piston, move by the piston, so, they have maximum displacement and form an antinode in displacement curve.
  • Air molecules at the closed end of the pipe remains stationary, and as a result, they form a node in the displacement curve.




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Pressure Oscillations


Close to displacement antinodes, particles move together and there is almost no change in the density of particles, thus, no change in the pressure. So, these points form nodes of pressure oscillation.

In contrast, particles close to the node has the maximum change in the density, thus, maximum change in the pressure. So, these points form antinodes of pressure oscillation.


Wize Tip
For sound waves, displacement oscillations and pressure oscillations are out of the phase by π2\frac{\pi}{2} such that nodes of one of them corresponds to the antinodes of the other one and vice versa.


Example: Pressure and Displacement


a) The following is a graph of the pressure along a sound wave. Draw the graph of the particle displacement on top of it.



b) The following is a graph of the pressure along a sound wave. Draw the graph of the particle displacement on top of it.



Points of max/min pressure correspond to zero particle displacement. Points of max/min particle displacement correspond to zero pressure (right in between the points of max/min pressure). Hence the π2\dfrac{\pi}{2} shift between them.

  • As we move along the x−x-axis from a min to a max pressure, the particles in that region are moving in the positive direction.
  • As we move along the x−x-axis from a max to a min pressure, the particles in that region are moving in the negative direction.

This means that the pressure is π2\dfrac{\pi}{2} ahead of the particle displacement, and particle displacement is π2\dfrac{\pi}{2} behind pressure.


Part a)


The pressure is π2\dfrac{\pi}{2} ahead of the particle displacement, so we should draw the displacement π2\dfrac{\pi}{2} units behind the pressure.




Part b)


The displacement is π2\dfrac{\pi}{2} behind the particle displacement, so we should draw the pressure π2\dfrac{\pi}{2} units ahead of the displacement.