class 37 wave motion...class 37 wave motion author rishi gopie created date 9/24/2014 4:29:58 am
TRANSCRIPT
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Mr Rishi Gopie WAVES
PHYSICS
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Mr R Gopie PHYSICS
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Wave Motion
A wave is a disturbance which is propagated in space (i.e. distance in a medium/vacuum)
and time by oscillations (i.e. vibrations). The frequency of waves produced by a source is the same
as that of the source itself.
Consider some types and examples of waves:
a) Progressive or travelling waves are associated with a net transfer of energy. Neighbouring
oscillations involved in their propagation have the same amplitude (if there is no loss of
energy). However, neighbouring oscillations are out of phase with one another.
b) Stationary or standing waves are associated with no net transfer of energy. Neighbouring
oscillations involved in their propagation do not have the same amplitude (even when there
is no loss of energy). In fact, at certain locations along the waves there are no oscillations
and such locations are called nodes. There are also certain locations at which the amplitude
is a maximum and such locations are called antinodes. All oscillations between adjacent
nodes are in phase with one another.
c) Transverse waves are produced by oscillations that occur perpendicularly to the direction
of propagation of the waves. Examples include electromagnetic waves (such as light waves,
radio waves etc.) and certain mechanical waves (such as waves on a string and on stretched
membranes.
d) Longitudinal waves are produced by oscillations that occur in a line that is parallel or
antiparallel to the direction of propagation of the wave. Examples include certain
mechanical waves such as sound waves and waves in springs (such as “slinky”) created by
to and fro movements along the length of the spring.
e) Waves can be produced in single pulses, for instance along a rope tugged up or down once
or as wave trains (i.e. a periodic, continuous waves such as sinusoidal waves. A pulse is a
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Mr R Gopie PHYSICS
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short-‐lived or single wave motion, while a wave train is a continuous group of waves with
features which repeat regularly. The shape of the pulses and wave trains remain the same
as they travel through a medium but their amplitude decreases as energy is lost and as the
waves spread out from a point source
f) Mechanical waves, require a material medium and examples include sound waves (as
produced by vibrating strings [guitars, pianos for instance], membranes [drums, steel pans
for instance] and air columns [in pipes/tubes such as flutes, trumpets, etc.]) and earth
quake shock waves. A mechanical wave is propagated by the collision of the particles of the
medium, but these do not themselves move along the wave.
g) Electromagnetic waves do not require a material medium and they can be propagated in a
vacuum. They include all the members of the electromagnetic spectrum such as gamma (γ)
rays, X-‐rays, u.v. radiation, visible light. I.R. radiation, microwaves, and radio waves. An E.M.
wave is not propagated by the oscillations of particles but by the oscillations’ of an electric
field and of a magnetic field (whose magnitude varies in both space and time). Consider an
oscillation about its equilibrium position.
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Diag. 1
A is the magnitude of the maximum displacement on either side of the equilibrium
position and is referred to as the amplitude of the motion.
An oscillation is a regular, periodic, to and fro, movement (or variation) about some
equilibrium (or central or rest or mean) position. The equilibrium position is that position
that would be occupied if the oscillations were to stop.
Consider 2(sinusoidal) wave forms (or wave profiles) which represent different aspects of
the same wave that is travelling in a medium (material or vacuum).
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a) A displacement – distance (or position) graph or wave form which represents the
instantaneous positions of several oscillations involved in the propagation of the wave:
Diag. 2
b) A displacement – time graph or waveform which represents a single oscillation involved
in the propagation of the wave as its displacement from its equilibrium position changes
with time.
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Mr R Gopie PHYSICS
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Diag. 3
A is the amplitude of the wave and is the maximum displacement of an oscillation
from its equilibrium position. It is also the peak (or maximum) value of the waveform
λ (lambda) is the wavelength of the wave and is the linear distance moved by the wave
in time of one period. It is also the linear distance between any two successive points on
the waveform (with respect to position/distance in the medium) that represent
identical phases of motion of different oscillations. T is the period of the wave and is the
time taken for the wave to travel through a distance of one wavelength. It is also the
time taken for a single oscillation to occur.
F is the frequency of the wave and is the number of the wavelengths or cycles
moved through, by the wave in once second. It is also the number of oscillations
occurring (at a given location) in one second. Its unit is Hz (i.e. Hertz) or s-‐1. V is the
speed of the wave and is the linear distance travelled by the wave in one second.
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Mr R Gopie PHYSICS
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Diag. 4
Consider two special phase relationships between waves:
a) Waveforms in phase – with crest -‐ on – crest and trough – on – trough:
Diag. 5
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Mr R Gopie PHYSICS
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b) Waveforms exactly out-‐of-‐phase (i.e. in antiphase), i.e. 180⁰ (or π radians)
Out – of – phase – with crest on trough and trough – on – crest:
Diag. 6
Wave fronts are line’s (straight or curved) joining points, on different
wavefronts, which are in the same phase of motion. Wavefronts can be used to
represent waves more simply. The linear distance between adjacent wavefronts
represent the wavelength (λ) of the waves, lines drawn through the wavefronts,
perpendicular to them all, are rays. Rays are the simplest way to represent waves –
but they simply indicate the direction (s) of propagation of the waves.
If the waveforms are parallel then the wavefronts associated with them are plane,
parallel wavefronts and the rays are parallel rays.
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Mr R Gopie PHYSICS
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Diag. 7
If the waveforms radiate from a point of disturbance (i.e. a point source)
then the wavefronts form a series of concentric circles and are known as circular
wavefronts. The rays associated with these wavefronts are divergent rays.
Diag. 8
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So waves can be represented most simply (but least usefully) by rays, less simply
(but most usefully by wavefronts and least simply (but most usefully) by
wavefronts.