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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   A piano wire is made of steel, with a diameter of 1.04 mm.
   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?