Major Concepts of Physics PHY102 – Lecture #2 12015Syracuse University

Lecture #2Lecture #2Everything about wavesEverything about waves

January 14January 14thth, 2015, 2015Prof. Liviu MovileanuProf. Liviu Movileanu

http://www.physics.syr.edu/~lmovilea/http://www.physics.syr.edu/~lmovilea/

MajorConceptsPhysics2015.htmlMajorConceptsPhysics2015.html lmovilea@syr.edu

Room 211, Physics Bldg., 443-8078Room 211, Physics Bldg., 443-8078

Major Concepts of Physics Major Concepts of Physics PHY102PHY102

Major Concepts of Physics PHY102 – Lecture #2 22015Syracuse University

1. To obtain a mechanistic understanding of the 1. To obtain a mechanistic understanding of the waveswaves

What is a wave?What is a wave? Examples…they are ubiquitousExamples…they are ubiquitous Understand the nature of waves. Types of Understand the nature of waves. Types of

waves waves Understand the simplest examples: the Understand the simplest examples: the

pendulum pendulum and spring (lecture demonstrations)and spring (lecture demonstrations)

2. To obtain a quantitative understanding of the 2. To obtain a quantitative understanding of the waveswaves

How are the waves described quantitatively?How are the waves described quantitatively? Get familiar with periodical expressions Get familiar with periodical expressions

describing describing waveswaves Simple harmonic motion (SHM)Simple harmonic motion (SHM)

Lecture objectivesLecture objectives

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The wave is a ubiquitous processThe 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 processThe wave is a ubiquitous process

Transfer of energy is accomplished in various ways

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Wave is a basic model of the Wave is a basic model of the worldworld

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 wavesTypes of waves

Transverse waves

Longitudinal waves

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Types of wavesTypes of waves

Transverse wavesLongitudinal (faster)

Transverse (slower)

Longitudinal and transverse wave motion at the surface

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Surface vs deep water wavesSurface vs deep water waves

Combination of transverse and longitudinal wavesCombination of transverse and longitudinal waves

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Quantitative understanding of Quantitative understanding of waves waves

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Periodicity of waves: time and spacePeriodicity of waves: time and space

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Harmonic waves are periodic waves in which the disturbance Harmonic waves are periodic waves in which the disturbance is sinusoidal (either a sine or cosine function)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 Harmonic waves are periodic waves in which the disturbance is sinusoidal (either a sine or cosine function)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 What parameters of the wave can you derive from this plot?can you derive from this plot?

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Practice this Practice this exampleexample

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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

Another exampleAnother example

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Simple Harmonic Motion (SHM)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 = - kxx is the displacement, or the distance of the mass from the equilibrium pointand k is a constant that depends on the system under consideration. The equilibrium point is considered at x=0

The units of k are: [k] =

Total energy=Kinetic energy + potential energy

m

N

22

22 mvkxEEE pktot

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Simple Harmonic Simple Harmonic MotionMotion

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 .

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Simple Harmonic Simple Harmonic MotionMotion

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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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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