Waves
Nature of Waves


Harmonic motion involved cyclic changes in position
over time.
Wave motion involves changes in position in time and
space.
Wave Properties

Waves have an amplitude.
• Maximum displacement from
equilibrium
A
Dx

Waves have a speed.
• Change in wave position with
time.
v = Dx / Dt

Waves can be a single pulse or a
continuous stream of pulses.
• Continuous waves have a period
Energy Transport

The points on the material don’t move with the wave.

The wave shape moves, and so does the energy.
Transverse Waves

A wave the undulates at right angles to the direction
of propagation is a transverse wave.
• Measure Dy(x,t)
1 wavelength
Dy
Time must be shown as
a sequence of graphs
x
Longitudinal Waves

A wave the undulates in the same direction of
propagation is a longitudinal wave.
• Measure Dx(x,t)
1 wavelength
Time must be shown as
a sequence of graphs
Dx
x
Water Waves

Some wave are combinations of longitudinal and
transverse waves.
• A point of water will travel in a circle (or ellipse)
The separation of peaks is
the wavelength l
The frequency of peaks in
space is the wavenumber k,
k = 2p/l
Wave Speed

For a continuous wave the
speed is the wavelength
compared to the period.
1 wavelength = l
v  l /T

On a string with some mass
the speed is related to the
tension.
v  FT m / L  FT / 
linear mass density = 
Rock Climbing

Two climbers are joined by a
43-m rope of 5.0 kg. One
climber strikes the rope and
1.4 s later the other climber
feels it.

v
FT / 
FT  v 2


The expression for tension is
The mass density and speed
  m/ L
What is the rope tension?
v  L /T
FT  mL / T 2

With values FT = 110 N
next