Traveling Waves

"The essence of science: ask an impertinent question, and you are on the way to a pertinent answer"
Jacob Bronowski

• Imagine a sequence of particles undergoing identical Simple Harmonic Motion, such that each particle begins to move slightly after the one before it.  The result is a traveling "Wave Motion".  If all the particles are connected, for example, in a string, the motion is described as a continuous "Sine Wave".

• The Sine Wave is the simplest of all possible waves.  A periodic wave is one in which the shape of the wave is repeated "periodically" - at regular fixed intervals.

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• Five basic properties which describe periodic waves.

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• Wavelength  ()  -  Distance after which the wave begins to repeat (Units: metres).
• Frequency (f)  -  Number of waves passing a fixed point in one second  (Units: Hertz).
• Wave period (T)  -  Time taken for one wave to pass a given point (Units: seconds).
• Wave speed (v)  -  Distance travelled by the wave per second  (Units: m/s).
• Amplitude (A)  -  Maximum displacement of particle which comprise the wave from their equilibrium position  (Units: metres).

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• Frequency, wavelength and speed are related by,

• There are two basic types of traveling waves.

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• TRANSVERSE   :  Motion of the constituent particles is at right angles to the wave direction, e.g. waves on a string, "stadium" wave, electromagnetic waves.

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• LONGITUDINAL   :  Motion of the constituent particles is back and forth in the direction of motion of the wave, e.g. sound waves, the " Slinky " spring.

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• Comparison of SHM and Waves

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• The amplitude of the SHM of the particles which comprise a Sine Wave is the same as the amplitude of the wave.
• The frequency of the SHM of the particles which comprise a Sine Wave is the same as the frequency of the wave.
• Particles which comprise the wave typically do not move at the speed of the wave, e.g. molecules of air do not move at the speed of sound  in air.

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• Miscellaneous important facts :

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• A wave "travels" from A to B.  The particles that comprise the wave do not move from A to B, they oscillate about their fixed (equilibrium) points.
• A wave transmits energy from one point to another.
• Water waves appear to be transverse  -  boats bob up and down due to water waves.  However,  a  detailed study shows that the molecules of water actually perform a circular motion, which can be considered as a combination of transverse and longitudinal wave motion.

•   Fourier's theorem states that any periodic wave can be decomposed into a sum of sine waves with differing frequencies and amplitudes.  This means that an analysis of the properties of sine waves can be applied to any periodic wave.

"In a packed program tonight we will be talking to an out-of-work contortionist who says he can no longer make ends meet."

Ronnie Barker

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu