Lecture #2 Waves and the Concepts Describing Them PHYS102

1. Lecture #2Waves and the Concepts Describing ThemPHYS102 January, 20th

2. Lecture objectives 1. To understand its basic concepts. 2. To understand what determines the values maintained by them. 3. To understand Single Harmonic motion (SHM) 4. Applications: The Spring and the Pendulum

3. 1. Time Oscillation A time oscillation is any motion that is repetitive. Preliminary Concept: 2. Example 1: Suspend a mass from a vertical spring. Displace the mass downward. Result: It oscillates back and forth with periodic motion. 3. Example 2: Vertical Pendulum 4. The displacement from the center-point of the motion is the “waving” or “oscillating” quantity. 5. Demos on computer – too much fun

4. First concept: The period T T is the repeat-time. The motion of a mass suspended from a spring has a simple name:Simple harmonic motion. Unit for period is: [T]= 1 s

5. Second Concept: The frequency f. This is the number of full cycles per time. Basic relation connecting these two concepts: f = 1/T. Unit for frequency is: [f]= [1/T] = 1 Hz (= 1 /s= 1s-1)

6. Spatial Oscillation: A spatial oscillation is represented by a quantity that changes along a particular direction, and is repetitive along that direction.

7. Third concept: The wavelength λ.This is the repeat-distance. Example: A tight rope is clamped at its two ends, and is horizontal. Unit for wavelength is: [λ] = 1 m

8. Pure Wave • Wavelength  disturbance  position

9. It is set into vibration. A snapshot is taken of the rope. The horizontal distance between points of maximum elevation is the wavelength.

10. Forth Concept: The wave-speed v. This is the speed at which the crests move The crest is any location at which the wave-value is largest.

11. 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

12. Simple Harmonic Motion 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 where the equilibrium position is chosen to have x -coordinate x = 0 and k is a constant that depends on the system under consideration. The units of k are: [k] = Total energy=Kinetic energy + potential energy

13. 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 . • 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. Simple Harmonic Motion

14. Pure Wave • Amplitude disturbance position

15. Homework (next week) http://wps.prenhall.com/esm_giancoli_physicsppa_6 Go to Chapter 11; Go to Practice Questions Click: submit answers for grading Send the results as email to: Rkincaid@phy.syr.edu, if the first letter of your last name is A, B…, M Amagri@phy.syr.edu, if the first letter of your last name is N, …, Z