PX154 - F1c - propagation

the wave speed

v = \frac{λ}{T} = f λ = \frac{ω}{k}

- where, $ω = 2 π f$ , and $k = \frac{2 π}{λ}$

comment:
- $v$ is also known as phase speed or phase velocity
- we have wave function $u (x, t)$ , but $\frac{\partial u}{\partial t} \neq v$

[YF p500]

transverse wave: vibrations of the particles are perpendicular to the direction of travel of the wave. modelling this transverse motion as SHM
longitudinal wave: vibrations of the particles are parallel to the direction of the travel of the wave. the particles are still doing SHM about a fixed position
our wave function, $u (x, t) = A \cos (k x - ω t)$ , tells us about the motion of the slinky itself. eg: for a transverse wave, this is only perpendicular to the wave's direction of travel. then:

\frac{\partial u}{\partial t} = A ω \sin (k x - ω t)

- this is not the speed of the wave