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Graphs Representing Waves
The following graphs represent continuous waves (as opposed to the single pulses shown here).  
These graphs have the same shape as graphs of sine of angle against angle.
For this reason the waves they describe are often called sine waves (or sinusoidal waves, if you want to sound more intelligent).  
This is the type of wave which results when the disturbance of the medium is produced by a body oscillating with simple harmonic motion, s.h.m.
   
Graph of Displacement of the Medium against Distance along a Typical Wave  
   
 
   
The maximum displacement of the medium from the equilibrium position, r, is called the amplitude of the wave.  
   
λ  is the wavelength.  
This is the distance moved by the disturbance during one time period (see below).  
   
For a transverse sine wave, this graph can be considered to be a picture of the wave at a given instant in time.  
However, it should be remembered that the graph could also represent a longitudinal wave.  
   
Graph of Displacement of a Particular Point in the Medium against Time for a Typical Wave  
   
 
 
T, is the time for one "cycle" of the wave.  
This is called the time period.  
   
The frequency, f, of the wave is the number of cycles per second.  
This is determined solely by the source of the waves (the frequency of a wave is equal to the frequency of the source).  
As with any cyclical phenomenon, the relation between frequency and time period is  
 
   
Relation between f, λ and Velocity of Propagation, v  
As stated above, λ is the distance moved by the disturbance during one time period.  
   
From the definition of velocity we have  
 
where s is distance moved and t time taken.  
So, in the particular case of a disturbance forming a wave we can write this as  
 
therefore  
 
This relation shows us that, for a given velocity, the wavelength is inversely proportional to the frequency.  
In other words, as frequency increases wavelength decreases.  
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