AP10005 - PhysI - Chap16 (Physic 1)

statics
AP10005 – Physics I
Lecture Set 3
Content Unit
Wave Motion 16
Oscillatory Motion 15
Sound Waves 17
Superposition and Standing Waves 18
*These materials are copyrighted to Cengage Learning and are restricted to personal use only
Your 7th online assignment
due 2 Nov, 12pm.
Transverse and longi
tudinal
waves 2
Chapter 16
Wave Motion
• To describe the propagation of a travelling wave

• To illustrate the factors related to the velocity of wave on a string
• To demonstrate reflection of waves
Types of Waves
Example of a wave
 Water waves, sound waves, light, etc.
There are two main types of waves.
 Mechanical waves
 Some physical medium is being disturbed.
 The wave is the propagation of a disturbance through a medium.
 Electromagnetic waves
 No medium required.
 Examples are light, radio waves, x-rays
3 Introduction
General Features of Waves
In wave motion, energy is transferred over a distance.

Matter is not transferred over a distance.
Mechanical Wave Requirements
• Some source of disturbance
• A medium containing elements that can be disturbed
• Some physical mechanism through which elements of the medium

can influence each other
4 Introduction
Transverse Wave
A wave is a periodic disturbance

traveling through a medium.
A traveling wave or pulse that causes
the elements of the disturbed medium
to move perpendicular to the direction
of propagation is called a transverse
wave.
 To create the wave, you would
move the end of the string up and
down repeatedly.
The particle motion is shown by the
black arrow.
The direction of propagation is shown
by the red arrow.
5 Section 16.1 animation

Longitudinal Wave
A traveling wave or pulse that causes the elements of the disturbed medium to
move parallel to the direction of propagation is called a longitudinal wave.
 Sound waves are another example of longitudinal waves (Chapter 17).
The displacement of the coils is parallel to the propagation.
6 Section 16.1
Transverse wave + Longitudinal Wave
Earthquake
7
Transverse and longitudinal waves
8
Wave function
At t = 0, the shape of the pulse is

represented by : y(x,0) = f(x).
It describes the transverse position y of

the element of the string at position x at
t = 0.
If the speed of the pulse is v, at the time

t the pulse will travel to the right by
distance vt. Then the wave function is:
y(x,t) = f(x-vt)
If the pulse travels to the left, then the

wave function at time t is:
y(x,t) = f(x+vt)
v is the speed of wave propagration,

9 NOT the motion of the elements.
Example 16.1
A pulse moving to the right

has the wave function:
10
Periodic Waves
optional
A sinusoidal wave is the simplest
example of a periodic continuous wave.
 It can be used to build more
complex waves (Fourier series).
11 Section 16.2
Spatial features of waves: Amplitude and Wavelength
The maximum displacement of the

element from the equilibrium position is
called the amplitude, A.
The wavelength, l, is the distance

from one crest to the next.
Traveling waves
12 Section 16.2
Temporal features of waves: Period and Frequency
The period, T, is the time interval required for the

element to complete one cycle of its oscillation and
for the wave to travel one wavelength (SI unit: s).
x 
Wave speed v 
t T
The frequency, ƒ, is the number of cycle

generated in 1 s (SI unit: s-1 = Hz).
The frequency and the period are related as:

1
ƒ
T
animation
13 Section 16.2
y(x,t) = f(x-vt)
• Vertical position versus horizontal • Vertical position versus time t

position x
• A graphical representation of the • A graphical representation of the
wave for a series of elements of position of one element of the
the medium at a give time. medium as a function of time.
14
x 
y(x,t) = f(x-vt) v 
t T
Set t = 0 at this moment

y(x,0) = Asin(ax)
aλ/2 = π
a = 2π/λ
• Vertical position versus horizontal

position x
  x t 
• A graphical representation of the y ( x, t )  A sin 2    
wave for a series of elements of    T 
15 the medium at a give time.
Wave Function
The wave function y (displacement of the element) can then be expressed as

  x t 
y ( x, t )  A sin 2    
   T 
This form shows the periodic nature of y (when x =  and/or t = T, the argument
inside gives a 2 which make y periodic).
y is a function of x (position) y is a function of t (time)
16 Section 16.2
Wave Function
The wave function can be expressed as:
  x t 
y ( x, t )  A sin 2     A sin kx  t 
   T 
If we define
2
k ,called the wave number, and

2
  2f ,called the angular frequency.
T
17 Section 16.2
Wave Function
y  A sin kx  t  [travelling in the +x direction]
y  A sin kx  t  [travelling in the -x direction]
The speed of the wave is:
 
v    f
T k
If y0 when x=0 & t=0, the wave function can be generalized to
y  A sin kx  t   
where  is called the phase constant.
18 Section 16.2
19 Section 16.2
Speed of a Wave on a String
The speed of the wave on a string, v, depends on the physical characteristics of

the string and the tension to which the string is subjected, i.e.
T
v

where T is the tension in the string (NOT period),  (= mass/length ) is the mass
per unit length (sometimes called the linear density) of the string.
20 Section 16.3
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21
Reflection of a Wave, Fixed End
When the pulse reaches the support,

the pulse moves back along the string
in the opposite direction. This is the
reflection of the pulse.
When the pulse is reflected from a
fixed end, it is inverted (180 phase
change).
 Due to Newton’s third law
 When the pulse reaches the
fixed end of the string, the string
produces an upward force on
the support.
 The support must exert an
equal-magnitude and oppositely
directed reaction force on the
string.
22 Section 16.4 animation

Reflection of a Wave, Free End
With a free end, the string is free to

move vertically.
When the pulse is reflected from a free

end, it is not inverted (0 phase
change).
animation
23 Section 16.4
Summary
24 Summary
Summary
25 Summary

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statics

• To describe the propagation of a travelling wave

In wave motion, energy is transferred over a distance.

Mechanical Wave Requirements

• Some source of disturbance

• A medium containing elements that can be disturbed

• Some physical mechanism through which elements of the medium

A wave is a periodic disturbance

5 Section 16.1 animation

 Sound waves are another example of longitudinal waves (Chapter 17).

The displacement of the coils is parallel to the propagation.

At t = 0, the shape of the pulse is

It describes the transverse position y of

If the speed of the pulse is v, at the time

If the pulse travels to the left, then the

v is the speed of wave propagration,

A pulse moving to the right

The maximum displacement of the

The wavelength, l, is the distance

The period, T, is the time interval required for the

The frequency, ƒ, is the number of cycle

The frequency and the period are related as:

• Vertical position versus horizontal • Vertical position versus time t

Set t = 0 at this moment

• Vertical position versus horizontal

The wave function y (displacement of the element) can then be expressed as

y is a function of x (position) y is a function of t (time)

y  A sin kx  t  [travelling in the +x direction]

y  A sin kx  t  [travelling in the -x direction]

The speed of the wave is:

The speed of the wave on a string, v, depends on the physical characteristics of

When the pulse reaches the support,

22 Section 16.4 animation

With a free end, the string is free to

When the pulse is reflected from a free

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