Major Concepts of Physics PHY102 – Lecture #  Syracuse University Lecture #2 Everything about waves January 14 th, 2015 Prof. Liviu Movileanu Room 211, Physics Bldg., Major Concepts of Physics PHY102

Major Concepts of Physics PHY102 – Lecture #  Syracuse University 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) Lecture objectives

Major Concepts of Physics PHY102 – Lecture #  Syracuse University The wave is a ubiquitous process Horrible things about waves The water waves The sound: a great example of waves

Major Concepts of Physics PHY102 – Lecture #  Syracuse University The wave is a ubiquitous process Transfer of energy is accomplished in various ways

Major Concepts of Physics PHY102 – Lecture #  Syracuse University 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.

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Types of waves  Transverse waves  Longitudinal waves

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Types of waves  Transverse waves Longitudinal (faster) Transverse (slower) Longitudinal and transverse wave motion at the surface

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Surface vs deep water waves Combination of transverse and longitudinal waves

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Quantitative understanding of waves

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Periodicity of waves: time and space

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Harmonic waves are periodic waves in which the disturbance is sinusoidal (either a sine or cosine function) Maximum speed Maximum acceleration

Major Concepts of Physics PHY102 – Lecture #  Syracuse University 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

Major Concepts of Physics PHY102 – Lecture #  Syracuse University What parameters of the wave can you derive from this plot?

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Practice this example

Major Concepts of Physics PHY102 – Lecture #  Syracuse University 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 example

Major Concepts of Physics PHY102 – Lecture #  Syracuse University 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: F s = - 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 The units of k are: [k] = Total energy=Kinetic energy + potential energy

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Simple Harmonic Motion 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 #  Syracuse University Simple Harmonic Motion 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.

Major Concepts of Physics PHY102 – Lecture #  Syracuse University 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, Wednesday, January 21 st, you will receive the first HW problemsAnnouncements