Energy density of 1-D longitudinal standing waves

cross-section

(in the yz-plane)

Strain:

density of the medium

(stress strain)

For a sinusoidal longitudinal standing wave,

where

Energy density of 1-D longitudinal travelling waves

Non-dispersive waves

t0 t1 t2

Different parts (colours) move with the same speed

Dispersive waves

t0 t1 t2

Different parts (colours) move with different speed

Dispersion relation

is independent of k for non-dispersive waves

is in general a function of k for dispersive waves

Some examples

dispersion relation

Phase and group velocities

As

Graphical representation

Vibration of a bar clamped at one end

A property of the bar

Water waves

surface tension of water, water density

Gravity waves:

Capillary waves (ripples):

Wave packets and pulses

t

y

x

y

y

xx

y

Superposition of waves