CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22 Course website: faculty.uml.edu/pchowdhury/95.141/ www.masteringphysics.com Course: UML95141SPRING2013 Lecture Capture h"p ://echo360.uml.edu/chowdhury2013/physics1Spring.html 95.141 Apr 29 , 2013 PHYSICS I Lecture 22
19
Embed
95.141 Apr 29 , 2013 PHYSICS I Lecture 22faculty.uml.edu/pchowdhury/95.141/Lectures/LECTURE22.pdf · Examples: wave on a string, water waves (on ocean, or ripples in pond), light
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
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
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
Exam 3 Sta>s>cs
Average 37.6%
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 10
# of
St
uden
ts Exam 3
FINAL EXAM on Mon May 6 8-11 am Olney 150
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
Simple Harmonic Motion
x = Acos(!t +")
v = dxdt= !!Asin(!t +")
a = d2xdt2
= !! 2Acos(!t +") = !! 2x
! =km
f = 1T
T = 2!"
period
amplitude displacement
frequency phase angle
angular frequency
spring-mass system
If we know x(t), we can calculate v(t) and a(t)
glT π2=simple
pendulum
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
1) 0 2) A/2 3) A 4) 2A 5) 4A
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 ?
Clicker Quiz
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
A) B) C) D) E)
A mass m is attached to a spring with force constant k as shown. The maximum speed of the mass is
Clicker Quiz
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
A km
A mk
A km
A2 km
A2 mk
λ wavelength
λ distance traveled by wave in one time period
Waves
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
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
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
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
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
Wave Properties Take snapshot of wave in time. Plot displacement vs. position.
x
t
T
Focus on a single point in space. Plot displacement vs. time.
λ
λ
T period
wavelength
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
• 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
Wave Properties
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
Let us freeze a wave in time, i.e. take a snapshot
D(x) = Asin 2!"x
!
"#
$
%&
Wave Math
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
The wave 1 s later
D(x, t) = Asin 2!"(x ! vt)
"
#$
%
&'
Wave has moved to the right by vt = 0.5m Curve iden>cal if shiQed back by a distance vt
Wave Math
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
The wave another second later (t=2s).
Wave has moved to the right by 1m.
Wave Math
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
The wave aQer 6s (t=6s).
Wave has moved to the right by one wavelength. Cannot dis>nguish it from its snapshot 6 s earlier!
Wave Math
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
D(x, t) = Asin 2!"(x ! vt)
"
#$
%
&' ! =
2"T
=2"v#
T = !v=2"#
k = 2!"
Wave Math
D(x, t) = Asin 2!"x ! 2!
Tt
"
#$
%
&'
D(x, t) = Asin kx !!t( )
wave number
wave traveling in +x direction
D(x, t) = Asin kx +!t( ) wave traveling in -x direction
T = 1f
k = 2!"
v = !T="k= ! f! =
2"T
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
ωT = 2π defines time period T
kλ = 2π defines wavelength λ
ω = 2π / T : angular frequency
k = 2π / λ : wave number
v = λ / T
v = ω / k
Wave Properties Review
D(x, t) = Asin kx !!t( ) D(x, t) = Asin 2!"x ! 2!
Tt
"
#$
%
&'
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
A) 6π B) 3π C) 2π/3 D) π/3 E) 0.1
A wave is described by where x and y are in meters, and t is in seconds. The wavelength (in meters) is:
Clicker Quiz
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
y(x, t) = 0.1sin(3x +10t)
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