PX154 - F1c - propagation

the wave speed

• in time, $T$, a wave peak moves a distance, $\lambda$
• to find the wave speed:

- where, $\omega =2\pi f$, and $k=\frac{2\pi }{\lambda }$

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

motion of the wave's substance

[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, $u(x,t)=A\cos (kx-\omega t)$, 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:

- this is not the speed of the wave

• for our wave: