Apr 29, 2013 PHYSICS I Lecture 22

Transcription

1 Apr 29, 2013 PHYSICS I Lecture 22 Course website: faculty.uml.edu/pchowdhury/95.141/ Course: UML95141SPRING2013 Lecture Capture h"p://echo360.uml.edu/chowdhury2013/physics1spring.html

2 Last Lecture Today Chapter 14 Simple Harmonic Motion Spring-mass & pendulum Chapter 15 Wave Motion Transverse Waves Longitudinal Waves Wave Math NEXT WED- LAST CLASS Mini-Review & Final Exam Discussion ATTENDANCE REQUIRED (WORTH 3X) RETURN CLICKERS COURSE/LECTURER EVALUATION

3 Exam 3 Sta>s>cs Exam 3 # of Students Average 37.6% FINAL EXAM on Mon May am Olney 150

4 Simple Harmonic Motion displacement amplitude angular frequency period T = 2! " frequency f = 1 T x = Acos(!t +") v = dx dt a = d 2 x dt 2 =!!Asin(!t +") =!! 2 Acos(!t +") =!! 2 x phase angle If we know x(t), we can calculate v(t) and a(t) spring-mass system! = k m simple pendulum T = 2π l g

5 Clicker Quiz A mass on a spring in SHM has amplitude A and period T. What is the total distance traveled by the mass after a time interval T? 1) 0 2) A/2 3) A 4) 2A 5) 4A

6 Clicker Quiz A mass m is attached to a spring with force constant k as shown. The maximum speed of the mass is A) A k m B) A m k C) D) E) A k m A 2 k m A 2 m k

7 Waves wavelength λ λ distance traveled by wave in one time period

8 Types of waves Transverse Wave: direction of displacement perpendicular to direction of wave propagation. Examples: wave on a string, water waves (on ocean, or ripples in pond), light waves Longitudinal Wave: direction of displacement parallel to direction of wave propagation Examples: sound waves, shock waves

9 Waves A periodic wave has a continuous oscillating source, e.g. a hand moving a piece of rope up and down Or a stereo speaker vibrating back and forth The source stays put, the displacement propagates. If we freeze the wave in time (take a snapshot) x

10 Wave Properties Take snapshot of wave in time. Plot displacement vs. position. λ x wavelength λ Focus on a single point in space. Plot displacement vs. time. T t period T

11 Wave Properties Amplitude (A): Maximum displacement from equilibrium. Wavelength(λ): Distance, in space, between successive crests (or troughs) of wave. Period (T): Time interval between successive crests or troughs at a fixed position Frequency (f=1/t): Number of crests passing through a fixed point per second. Velocity (v= λ/t=λf): wave travels a distance of one wavelength in a time interval of one period

12 Wave Math Let us freeze a wave in time, i.e. take a snapshot! D(x) = Asin# 2! " " x $ & %

13 The wave 1 s later Wave Math Wave has moved to the right by vt = 0.5m Curve iden>cal if shiqed back by a distance vt " D(x,t) = Asin$ 2! % (x! vt) ' # " &

14 Wave Math The wave another second later (t=2s). Wave has moved to the right by 1m.

15 The wave aqer 6s (t=6s). Wave Math Wave has moved to the right by one wavelength. Cannot dis>nguish it from its snapshot 6 s earlier!

16 Wave Math " D(x,t) = Asin 2! % $ (x! vt) ' T =!! = 2" # " & T = 2"v v = 2" # # " D(x,t) = Asin$ 2! " x! 2! # T t % ' & D(x,t) = Asin( kx!!t) k = 2! " wave number wave traveling in +x direction D(x,t) = Asin( kx +!t) wave traveling in -x direction T = 1 f! = 2" T k = 2! " v =! T = " k =! f

17 Wave Properties Review D(x,t) = Asin kx!!t ( ) D(x,t) = Asin$ 2! " x! 2! T t " # % ' & ωt = 2π defines time period T kλ = 2π defines wavelength λ ω = 2π / T : angular frequency v = λ / T v = ω / k k = 2π / λ : wave number

18 A wave is described by y(x, t) = 0.1sin(3x +10t) where x and y are in meters, and t is in seconds. The wavelength (in meters) is: A) 6π B) 3π C) 2π/3 D) π/3 E) 0.1 Clicker Quiz

19 Summary Simple Harmonic Motion Review Wave Motion Transverse Waves Longitudinal Waves Wave Math NEXT WED- LAST CLASS Mini-Review & Final Exam Discussion ATTENDANCE REQUIRED (WORTH 3X) RETURN CLICKERS COURSE/LECTURER EVALUATION