Notes on the lecture “4 – Waves” slides
Slide #2
(Cambridge Dictionary on-line)
- heat wave: a period of time such as a few weeks when the weather is much
hotter than usual
- Mexican wave : a wave-like movement made by a crowd watching a sports
game, when everyone stands and lifts up their arms and then sits down again
one after another
- crime wave: a sudden increase in the number of crimes
- be riding on the crest of a wave: to be very successful for a limited period of
time
Slide #3
Definition of wave (Cambridge Dictionary on-line): the pattern in which some
types of energy, such as sound, light and heat, are spread or carried.
A common naïve ideas is that any wave carries matter when it travels. This idea is
not correct in terms of physics knowledge. Likely it may be originated by the
observation that, for mechanical waves, the small parts of the medium do move up
and down, i.e. they oscillate from their equilibrium position.
In several textbooks it is suggested to observe the movement of a small piece of
material (e.g. cork, wood, …) floating in water waves: it oscillates up and down
remaining always at its place. But sometimes, specially at sea or lake, it is
common to observe the cork translating and reaching the beach. This translation is
due to a complex feature of the waves in shallow water, does not mean at all that
wave carry matter.
Slide #4
The harmonic oscillations are “free” when friction is negligible. The case of no
friction is an ideal case; the oscillation amplitude remains constant and the motion
goes on for ever.
In case of not negligible friction the oscillations are affected by dumping, i.e. the
amplitude reduces in time until the system does not move any more, as the
commonsense knowledge teaches.
The dumping produces dissipative effects; it can be caused by friction at the
suspension, resistance of the medium the system moves through, any other source
of friction. The oscillations of real systems are always damped, but in some cases
the dumping is small, so for a limited interval of time the behaviour of the system
can be approximated as if it was that of a free harmonic oscillator.
Slide #5
The figure shows a water wave; it is easily produced in a container filled with
water by immerging rhythmically a finger, a pencil, a stick, …
Arrange this “no-cost” lab experiment : call the attention of your students on what
is observable, specially when small, light pieces of floating materials are on the
water; ask them to describe their observations in common words and keep track of
their phrasing.
Slide #6
The crest is the point where the amplitude of the oscillation is maximum.
The trough is the point where the amplitude of the oscillation is minimum.
Slide #7
A common misunderstanding is the confusion between the oscillatory motion of
the medium particles (small portions of the medium) with the motion of the wave,
i.e. how the disturbance in the medium propagates.
The medium particles oscillates up and down (in a transverse wave, cfr. later)
around their equilibrium position.
The wave, i.e. the deformation of the equilibrium pattern of the medium,
propagates from the wave source onward.
A simple “no-cost” experiment can be easily done with a piece of rope hold at its
ends. A transverse wave can be excited on the rope by pulling it at a point and
leaving it suddenly. The wave propagates along the rope.
Ask the students how they would produce a wave on the rope and note these
predictions.
To observe that the single small portions of the rope oscillates up-down it is useful
to identify some points by gluing to them a small piece of paper or of a sewing
thread, or colouring them.
Ask the students to observe, describe the observation in their common word and
take note of these descriptions.
Slide #8
Sound waves are mechanical waves, a medium is needed to produce them. Sound
does not exists in vacuum.
Light is an electromagnetic wave (cfr. later). i.e. a transversal wave whose
oscillating entities are electric and magnetic fields.
Differently from mechanical waves (water waves, rope waves, sound, ..) NO
medium is needed to generate an e.m. wave that can propagate in vacuum and in
media.
Slide #9
Cambridge Dictionary on-line: transverse wave in physics, a wave moving
through a substance in which the particles are vibrating (= moving quickly
backwards and forwards) at a 90 degree angle to the direction of the wave
Slide #10
Mechanical longitudinal wave (Cambridge Dictionary on-line):
in physics, a wave moving in the same direction of travel as the vibrations (= fast
movements backwards and forwards) of the particles of the substance through
which it is traveling.
Slide #11
Transversal waves have a property which the longitudinal ones have not: they can
be polarised (cfr. later). For transversal waves it is possible to define a plane by
two lines: the direction of the wave motion and that of the oscillating entities. For
longitudinal planes this is not possible, being these two directions identical. The
above plan is needed to define the polarization of the wave. The longitudinal
waves cannot be polarised.
Slide #13
Definition An ideal wave is infinite, the real ones are always finite, starting
somewhere and ending somewhere else because of inevitable dissipative effects
(all real waves are affected by dumping)
A travelling impulse is a non periodic wave. i.e. a short wave with no repeated
oscillations.
Slide #14
The The case b) of the figure is an ideal, infinite wave; the c) represents a real
case, i.e. a finite wave or a train wave with a starting and an ending point
Slide #18
The crest, point where the wave amplitude is maximum, moves along the direction
of the wave motion, with a speed equal to that of the wave. This is true also for the
valley, the point where the wave amplitude is minimum, and also for any other
point of the wave shape.
Slide #21
For every type of wave it is possible to identify a wave front. It is the locus (a line
or surface) of all points having the same phase.
Slide #24
The Superposition Principle holds anytime the equation of the studied system are
linear. Namely for such equations, any linear combination of solutions is still a
solution. The wave equation is a linear one.
Slide #25
When two waves of same amplitude interfere destructively, the resulting
amplitude is zero, as in the shown applet.
Slide #26
Electromagnetic waves are produced by accelerated charges; they are transversal
waves NO medium is needed to produce an e.m. wave; they propagate also in
media.
The oscillating entities are E and B, respectively electric and magnetic field
The speed of e.m. waves in vacuum is c = speed of light = 300.000 km/s, the
maximum speed in our universe.
The speed of e-m. waves in media is less than c
Slide #27
The e.m. Waves is very broad, from radio waves to gamma rays; their frequency
span a range of about 13 orders of magnitude.
They can be described in terms of frequency or in terms of wavelength; the
translation between these two languages is via lambda = c / frequency.
At the bottom of the figure some everyday life lengths to give a feeling for order
of magnitude of wavelengths of same regions of the e.m. spectrum.
Slide #28
The visible light range is a very small interval of the e-m-spectrum. The humans
biological e.m. detectors do “see” only visible light.
Some animals “see” also in the infrared region, so they hunt at night detecting the
warm bodies of their preys.
Slide #29
In Optics two languages or models can be used: a) the ray one where a ray is a
mathematical schematization of a very thin beam; b) the wave front model
Connection between these two models: a ray is a line ALWAYS orthogonal to the
wavefront.
Slide #30
The frequency of any wave (here the specific case of light) CANNOT change
when the wave propagates from one medium to a different one, because the wave
source has emitted the wave at that frequency and there is no way of changing the
value of f apart from interaction with the source.
Ex: the Sun emits visible light, its frequency cannot be changed unless it is
possible to influence the light production by the Sun.
Slide #32
Transversal Short wavelengths are perceived as blue, longer ones as red. Green is
in between.
Speed of light is slower in glass or water and slightly different for different
wavelengths! Basis of prism and rainbow.
Slide #34
In the figure, for graph clarity only three wavelengths have been displayed.
Slide #29
In Optics two languages or models can be used: a) the ray one where a ray is a
mathematical schematization of a very thin beam; b) the wave front model
Connection between these two models: a ray is a line ALWAYS orthogonal to the
wavefront.