# Notes on wave motion

• 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)
```
• 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 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?

```