- 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 beω 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 of1.04 mm.The wire is stretched inside the piano to a tension of400 N. Q: How fast do vibrations travel down this wire? Q: This particular wire is1.2 mlong. 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?