Physics 1051 – Lecture 4
Mechanical Waves
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
Lecture 03 - Contents
13.0 Introduction to Mechanical Waves
13.1 Propacation of a Disturbance
13.2 The Wave Model
13/06/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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13.0 Introduction to Mechanical Waves
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Examples of waves are all around us
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Water waves
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Vibration on a guitar string
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Sound
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Light
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Mechanical Waves
Electromagnetic Waves
Radio
Two categories of waves
1 Mechanical Waves
2 Electromagnetic Waves
13/06/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
3
Mechanical Waves
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What is a wave?
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Two distinct things happening in a wave
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Disturbance Moves
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Element of Medium Moves
Note: The difference in these two is subtle and we
will discuss it further...
13/06/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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13.1 Propagation of a Disturbance
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Wave motion: transfer of a
disturbance through space
without any transfer of matter.
Mechanical Waves require:
1 a disturbance
2 a medium (to be disturbed)
See
Figure 13.1
and
Figure 13.2
3 a physical mechanism where
elements can influence one
another (propagation of
disturbance)
13/06/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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Types of Mechanical Waves
There are two types of Mechanical Waves:
1 Transverse: element of medium is disturbed
and moves in a direction perpendicular to
See Figure 13.2
direction of propagation
2 Longitudinal: element of medium is disturbed
and moves in a direction parallel to direction of
propagation
See Figure 13.3
13/06/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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Mathematical Representation
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We want to describe this wave,
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i.e. shape for all time
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i.e. vertical position of all elements at each position
yx ,t
Looking for general form of a function f  x , t 
See Figure 13.4
that describes y  x , t 
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Let's look at a wave moving with
constant velocity v =v x i
We are going to use a model where shape
doesn't change (in real life it does)
13/06/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
7
“The Wave Function”
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Start by writing mathematically that shape stays
the same as the initial one
y  x , t = y  x i , t i 
x = x v t
f
y  x , t = y  x−v x t , 0
y  x , t = f  x−v x t 
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i
xi
x i = x f −v x i t
x i = x−v x t
This is the general form of the wave function for
constant velocity (both directions)
A wave moving to the right y  x , t = f  x−vt 
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13/06/10
A wave moving to the left
y  x , t = f  xvt 
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
8
Example
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Problem 13.2, page 425
Ocean waves with a crest-to-crest distance of
10.0 m can be described by the wave function
y x , t=0.800 msin [0.628 x−vt]
where v = 1.20 m/s.
(a) Sketch y(x,t) at t=0s
(b) Sketch y(x,t) at t=2.00s
(c*) Which direction is the wave moving?
(d*) What is the displacement?
13/06/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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13.2 The Wave Model
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Waves and S.H.M. are NOT the same thing but
there are connections/similarities
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A continuous wave is generated by S.H.M.
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e.g. sound wave, wave on a string
Sinusoidal Wave, a wave with shape of sine
function, is formed
Crest: position of largest positive
displacement
Trough: position of largest positive
displacement
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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Physical Characteristics of Sine Wave
 [SI units: m]
1 Wavelength
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Wavelength: the minimum
distance between any two
consecutive “identical” (same y
and v) points on a wave
2 Frequency
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f
13/06/10
[SI units: Hz]
same as S.H.M. (inverse of
period)
3 Wave Speed
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See Figure 13.6 (a)
v
[SI units: m/s]
wave speed: speed of disturbance
(depends on the medium)
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
11
Physical Characteristics of Sine Wave
4 Period
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T
period: time for one complete
oscillation
5 Amplitude
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[SI Unit: s]
A
See Figure 13.6 (b)
[SI Unit: m]
amplitude: is the distance from
maximum position to the
equilibrium condition
1
T=
f
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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Way to Produce Travelling Wave
See Figure 13.7
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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Note on the Wave Model
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In the physics before now we treated
complicated objects by simplifying them as
particles
The same can be done for waves
An ideal wave is one that has a single
v, A.
, f ,
We will use this later to look at more
complicated waves like non-sinusoidal waves in
section 14.7
13/06/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
14