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  -  ω*t )
but provide the numerical values for all constants, in standard SI units.

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.

  1. How fast do vibrations travel down this wire?
  2. This particular wire is 0.6 m long. How long does it take a wave to travel from one end to the other, and then back again?
  3. Can you guess the note this wire will produce?
  4. Leopold demands that this wire produce a perfect A-note, with frequency 220 Hz. What do you do?