Notes on wave motion

• Viewgraph 1

• Viewgraph 2

  Don't forget k = wave number .

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

• Viewgraph 3

• Viewgraph 4

• Viewgraph 5

• Viewgraph 6

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

  
                    sin (kx - ωt)
        

  then the wave speed will be

  
                            ω
                      v  = ---
                            k
        

• Viewgraph 7

  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 ....
  
  

  ---

• Viewgraph 8

• Viewgraph 9

• Viewgraph 10

• Viewgraph 11

 




   A piano wire is made of steel, with a linear mass 
   density of μ = 0.00574 kg/m. The wire is stretched inside 
   the piano to a tension of 400 N.

   
     Q:  How fast do vibrations travel down this wire?




     Q:  This particular wire is 1.2 m long.  
         How long does it take a wave to travel from one 
         end to the other?




     Q:  Can you guess the note this wire will produce?