Major Concepts of Physics PHY102
Lecture #2
Everything about waves
January 14th, 2015
Prof. Liviu Movileanu
http://www.physics.syr.edu/~lmovilea/MajorConceptsPhysics2015.html
lmovilea@syr.edu
Room 211, Physics Bldg., 443-8078
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Lecture objectives
1. To obtain a mechanistic understanding of the waves
 What is a wave?
 Examples…they are ubiquitous
 Understand the nature of waves. Types of waves
 Understand the simplest examples: the pendulum
and spring (lecture demonstrations)
2. To obtain a quantitative understanding of the waves
 How are the waves described quantitatively?
 Get familiar with periodical expressions describing
waves
 Simple harmonic motion (SHM)
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The wave is a ubiquitous process
Horrible things about waves
The water waves
The sound: a great example of waves
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The wave is a ubiquitous process
Transfer of energy is accomplished in various ways
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Wave is a basic model of the world
The wave is a fundamental and ubiquitous feature of
matter. It has a mechanical nature.
It represents any physical process that propagates
periodically or exhibits periodicity.
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Types of waves
Transverse waves
Longitudinal waves
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Types of waves
Transverse waves
Longitudinal (faster)
Transverse (slower)
Longitudinal and transverse wave motion at the surface
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Surface vs deep water waves
Combination of transverse and longitudinal waves
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Quantitative understanding of waves
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Periodicity of waves: time and space
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Harmonic waves are periodic waves in which the disturbance
is sinusoidal (either a sine or cosine function)
Maximum speed
Maximum acceleration
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Harmonic waves are periodic waves in which the disturbance
is sinusoidal (either a sine or cosine function)
The motion of the point x repeats the motion of the point x=0 with a time delay t=x/v
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What parameters of the wave can
you derive from this plot?
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Practice this example
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Another example
The basic relation underlying all waves:
Wave-speed equals frequency times wavelength.
In symbols, v = fλ.
This equation is called the wave-relation.
Unit for wave-speed is: [v] = 1 m/s
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Simple Harmonic Motion (SHM)
Idea: Any object that is initially displaced slightly from a stable equilibrium
point will oscillate about its equilibrium position. It will, in general,
experience a restoring force that depends linearly on the displacement
x from equilibrium: Hooke's Law:
Fs = - kx
x is the displacement, or the distance of the mass from the equilibrium point
and
k is a constant that depends on the system under consideration.
The equilibrium point is considered at x=0
N
The units of k are: [k] =
m
kx2 m v2
Etot  Ek  E p 

2
2
Total energy=Kinetic energy + potential energy
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Simple Harmonic Motion
Definitions:
•Amplitude (A): The maximum distance that an object moves from its
equilibrium position. A simple harmonic oscillator moves back and forth between
the two positions of maximum displacement, at x = A and x = - A .
•Period (T): The time that it takes for an oscillator to execute one complete
cycle of its motion. If it starts at t = 0 at x = A , then it gets back to x = A after
one full period at t = T .
Major Concepts of Physics PHY102 – Lecture #2
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Simple Harmonic Motion
Definitions:
•Frequency ( f ): The number of cycles (or oscillations) the object
completes per unit time. f = 1/T
The unit of frequency is usually taken to be 1 Hz = 1 cycle per second.
•Simple Harmonic Oscillator: Any object that oscillates about a stable equilibrium
position and experiences a restoring force approximately described by Hooke's law.
Examples of simple harmonic oscillators include: a mass attached to a spring,
a molecule inside a solid, a car stuck in a ditch being ``rocked out'' and a pendulum.
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Announcements
1. The coming week, we will have the first workshop, titled
“Introduction to waves and resonance”
2. Read the print outs, except sections 11.3, 11.7, 11.8
3. Wednesday, January 21st, you will receive the first HW problems
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