Wave Motion I

• Transverse waves feature displacement perpendicular to the direction of wave motion.
• Longitudinal waves feature displacement parallel to the direction of wave motion.
• A travelling wave must have form f(x - vt)
• When two waves meet, the result is the algebraic sum of the individual wave equations; this is the Principle of Linear Superposition
• A wave moving a string of linear mass density mu, and tension force F, has speed

            v = sqrt(F/mu)
  

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  Don't forget k = wave number .

  
  
                       2 * pi
             k   =   -----------
                     wavelength
       
     

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  So, if we have a wave written in the standard form

  
                    sin (kx - ωt)
        

  then the wave speed will be

  
                            ω
                      v  = ---
                            k
        

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  Challenge Problem: An earthquake hits Los Angeles! A wave ripples down the LA Freeway at a speed of 150 mph, with crests 60 m apart. Motorists caught by the quake are shaken up and down inside their cars violently. The road moves so quickly that, after pushing cars up to a peak height at a crest, the asphalt almost leaves the tires behind as they fall into a trough.

  Write an equation for this wave of the form

  
         y(x, t)  =   A  *  sin ( k*x  -  omega*t )
     

  but provide the numerical values for all constants, in standard SI units.

  
  
  
  
  
  
  
  
    Now is a good time for physlets ....
  
  

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