Properties of Waves: Wave Representation


Representing longitudinal waves graphically


As can be seen in the simulation below, transverse and longitudinal waves look very different. However, the graphs of displacment versus position along the direction of wave travel are actually very similar. Start and pause the simulation below show. If you wanted to plot the displacement of the string as a function of position along the string for the top transverse wave, the graph would look just like the string. This can cause confusion because students may assume that plots of waves are the same as pictures of waves!

  In the case of the tranverse wave on a string, the direction of the displacment is perpendicular to the distance along the string. However, when we make a plot, the fact that the vertical axis is perpendicular to the horizontal axis does not necessarily mean that the quantity plotted in the vertical axis is perpendicular to the quantity plotted on the horizontal axis! In fact, if we plot something like temperature versus position, we realize the the quantity in the vertical axis may not even be of the same type (in this case, a distance/position) as the quantity on the horizontal axis!

  Look at the motion of the air molecules in the sound wave below and think about graphing the displacement of air molecules as a function of position for the longitudinal sound wave?


  If we plot the displacements of air molecules as a function of position along the sound wave's travel direction, the graph looks like a transverse wave. Although the displacements are parallel to the wave travel direction in a longitudinal wave, the graph's vertical axis represents the displacement and the horizontal axis represents the distance along the wave's direction of travel. Although the graph looks like a transverse wave, we must remember that in the case of a longitudinal wave, the displacements are actually along the direction of travel!

  The simulation below shows how a longitudinal wave is plotted as a transverse wave when sound is picked up by a microphone. The microphone produces an electrical voltage that is proportional to the pressure of the air that surrounds it. In this case, higher pressure air produces higher voltages and lower pressure air produces lower voltages. As the alternating pressure regions of the sound wave strike the microphone, the microphone voltage oscillates. An oscillosope plots the voltage produced by the microphone as a function of time on a screen. Note that the plot looks like a transverse wave, but realize that the plot is just an abstract representation of the wave, not a picture of the wave.

  Please turn on the sound on your computer so that you can hear the sound wave that is picked up by the microphone and correlate the oscilloscope plot to the sound wave.