Waves are everywhere:

1
Waves are everywhere Earthquake, vibrating
strings of a guitar, light from the sun a wave
of heat, of bad luck, of madness
Something moving, passing by, bringing a change
and than going away, sometimes without a trace
Some waves are man-made radio waves, stadium
waves, microwaves, annoying sound waves of a
physics lecture amplified by the electronics and
loudspeakers
2
A wave is a traveling disturbance that transports
energy but not matter.

• Mechanical waves require
• Some source of disturbance
• A medium that can be mechanically disturbed
• Some mechanism through which adjacent regions of
  the medium influence each other
• All waves carry energy and momentum

The stadium "wave" travels all around the
stadium. None of the fans travel around the
stadium. They only stand up and sit down.
3
Well, lets forget about humans and talk about
passively floating objects and the impact waves
make on them.
Imagine, you are a happy seal on a buoy. It is
nicely warm and you closed your eyes.What kind
of motion are you going to experience?
The buoy and the seal are going to bob on the
waves and its motion can we well described by a
harmonic oscillation.
Any way to find out that you are actually in sea
rather than on a shaking platform?
4
NO! An observer recording motion in a single
point in space only sees a harmonic oscillation
and there is no way to know, whether or not there
are waves.
How can he find out that he is shaking on waves?
To look out and take a photograph (or to see what
happens around him).
The complex nature of a wave it is an
oscillation in time and a wavy pattern in space!
Lets do the oscillation part first.Oscillations
have amplitude and frequency.Any way to measure
them without looking out?
You can measure frequency and accelerationAnd
use them to derive the amplitude.
http//www.phy.ntnu.edu.tw/java/Pendulum/Pendulum.
html
5
Harmonic oscillation - the motion is sinusoidal
- height of the object with respect to its
equilibrium position amplitude of the
oscillations angular
frequency, measured in rad/s
regular frequency, measured in Hertz (cycles
per second) or s-1 the period of
oscillations in seconds
What about velocity and acceleration?
6
Harmonic oscillation - the motion is sinusoidal
can be defined as the amplitude of
oscillations of the velocity
can be defined as the amplitude of
oscillations of the acceleration
From measurements the maximal acceleration and
the period, we can calculate the frequency and
the amplitude of the oscillations.
7
How is the frequency connected to the parameters
of the system?
Spring elasticity the restoring spring force, F,
where y is the deviation from the equilibrium
position
An oscillation (and a wave!) requires a restoring
force elastic tension in the spring in this
case.The larger the restoring force (the
tougher the spring) the faster it goes (the
higher is the frequency of oscillation)A large
mass (inertia) of the oscillation object slows
the oscillations down (reduces the frequency).
8
Energy of oscillations potential and kinetic.
Potential energy
Kinetic energy

• Both energies are proportional to the amplitude
  squared They both reach maxima twice per
  cycle They both are always positive and their
  sum remains constant They oscillate out of
  phase with each other.

9
Waves have all the same stuff as the oscillation
doamplitude, frequency, energyBut they also
have much more, because they propagate in space
Too bad for you, fellows ?
l
The two basic new parameters arewave length and
wave speed.
10
How do we define the wave speed?
L
If two point are a distance L apart and it takes
a wave crest a time t to travel between them, the
wave speed, v, is calculated asIt is just a
regular definition of speed - how fast the wave
crest travels.
11
How do we calculate the speed of a traveling wave?
l
Two polls placed the wavelength, l, apart.The
oscillations there are always in phase. The time
it takes a crest to travel between them is the
period of oscillations T (exactly the time
between two consecutive crests at a
point!).Therefore the wave speed, v, can be
calculated as.
12
Wave motion (a traveling wave)
L
l
There is NO direct connection between the wave
speed, and the velocity of motion of material
particles,
13
Longitudinal Waves
In a longitudinal wave the particle displacement
is parallel to the direction of wave propagation.
The animation above shows a one-dimensional
longitudinal plane wave propagating down a tube.
The particles do not move down the tube with
the wave they simply oscillate back and forth
about their individual equilibrium positions.
Pick a single particle and watch its motion! The
wave is seen as a motion of compressed regions
(i.e. it is a pressure wave), which move from
left to right.
14
Transverse vs. longitudinal waveBoth propagate
from left to right, but cause disturbances in
different directions, Dy and Dx.
amplitude
wavelength, l
amplitude
wavelength, l
Normally the amplitudes of (harmonic) motion of
the particles are much smaller than the
wavelength.
15
Longitudinal spring waves
16
Waves on a Spring