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Graphical Representation of Waves

We can show that both longitudinal and transverse waves can be represented by a displacement-distance graph.  If we take a snapshot of a wave at any instant, we see:

For a transverse wave we see that the graph looks very similar to the actual wave.

For a longitudinal wave the graph is not so easy to see.

Let us look at the air molecules in their undisturbed positions and compare them as a sound wave passes by.

If we plot displacement on the y-axis and distance on the x-axis, we get the same graph to what we had before.   The shape is a sine wave.

If we plot a displacement-time graph for a single particle we see:

This is true whether we have a longitudinal or transverse wave.  If we connect a microphone to a CRO, the CRO displays a displacement-time trace.  It is important that we do not confuse the displacement-distance with the displacement-time graph. The latter tells us nothing of the wavelength, only the period (hence the frequency) of the wave.

The simplest shape of graph we see is the sine wave.  The sine wave equation links wave motion with simple harmonic motion.   Sine waves in sound are very boring to listen to.  The quality of the sound gives us important clues as to the source.  Sounds made by different musical instruments have very different wave patterns, even if the notes sounded and the volumes are the same.

Question 9

The diagrams show the variation with time t of the displacement x of the two identical cones of loudspeakers A and B in air.

Calculate:

(a)    the frequency of the vibration of the speaker cones.

(b)   the phase difference between the speaker signals.

(c)    What kind of wave is being produced in the air by each speaker?

(d)   Which speaker produces the loudest sound?  Explain your answer.

(e)    The speed of sound in air is 340 m/s.  What is the wavelength of the sound waves?

ANSWER

How much do you know about Transverse and Longitudinal Waves?  Click HERE

 

Summary

  • Waves transfer energy without transferring material.

  • Waves have a wavelength and amplitude.

  • The movement of particles is at right angles to the direction of movement in a transverse wave.

  • The movement of particles is parallel to the direction of movement in a longitudinal wave.

  • Wave equation: c = fl

  • Waves can be represented graphically.

  • Graphs of two waves can show phase difference.

  • Transverse waves can be polarised, longitudinal waves cannot.

 

                                          

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