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CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
Course website: faculty.uml.edu/pchowdhury/95.141/
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Course: UML95141SPRING2013
Lecture Captureh"p://echo360.uml.edu/chowdhury2013/physics1Spring.html
95.141 Apr 29 , 2013 PHYSICS I Lecture 22
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
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
Exam 3 Sta>s>cs
Average 37.6%
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1 2 3 4 5 6 7 8 9 10
# of
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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
CHOWDHURY 95.141 PHYSICS I SPRING 2013 LECTURE 22
