Wave motion Chapter for 12

1. Wave Motion

2. What’s the first thing that comes to mind when you
hear the word “wave”? We often think of common
forms of waves such as the waves in the ocean. But
there are many kinds of waves. Waves are all around
us and we encounter them everyday. There are light
waves, sound waves, and many more. In this section,
we are going to look at common types of waves, what
parts make up those waves, and real life examples of
waves.
Introduction to Waves

3. Amplitude is a measurement from
equilibrium to the crest of a wave.
Equilibrium is the point half way in
between a crest and a trough in
the vertical direction. We measure
to the crest instead of the trough
because then the amplitude is a
positive number. Amplitude is a
measure of the intensity of a wave.
The symbol for amplitude is A and
it is measured in meters.
Amplitude

4. The wavelength is the
length of one complete
wave, or cycle. It is
measured from crest to
crest or from trough to
trough for transverse
waves. It is similar for
longitudinal waves as well.
The symbol for wavelength
is the Greek letter lambda
(λ) and is measured in
meters.
Wavelength

5. Period
Period is the time it
takes to complete one
full cycle of a wave. A
cycle is from rarefaction
to rarefaction or from
compression to
compression for
longitudinal waves. It is
similar for transverse
waves as well. The
symbol for period is T
and it is measured in
seconds.

6. Frequency is the
number of cycles that
occur for every unit of
time. There are two
equations for
frequency. These are
used to make
calculations with waves.
The symbol for
frequency if f and it is
measured in cycles per
second.
Frequency
Frequency is the inverse of period:
Frequency is equal to the velocity of
a wave divided by the wavelength:

7. The crest is the highest
point in the vertical
direction for a
transverse wave.
Similarly, the trough is
the lowest point in the
vertical direction.
Crests and Troughs

8. The compression of a
longitudinal wave is the
part of the wave where
the particles in a wave
are most dense.
Rarefaction is the part
of the wave where the
particles are least
dense.
Compression and Rarefaction

9. There are many types of
waves. In this section, we’re
specifically going to look at
transverse waves and
longitudinal waves, as well as
examine a special type of wave
called a standing wave. They
are examples of mechanical
waves. An important concept
about wave motion is that
waves transfer energy, NOT
matter.
Types of Waves

10. A transverse wave is
characterized by
particle motion that is
perpendicular to the
wave energy. It is
important to
understand that an
individual particles do
not move from there
original position on the
horizontal axis, they
merely oscillate
vertically.
Transverse Waves
Click on the picture to visit a website
that let’s you adjust the wavelength
and amplitude of a transverse wave.

11. A longitudinal wave is
characterized by
particle motion that is
parallel to the direction
of the wave energy.
Even though they are in
the same direction, it is
important to note that
a particle does not
move with the wave, it
merely oscillates in the
same direction.
Longitudinal Waves
Click on the picture to visit a website
that shows animated pictures of wave
motion.

12. The simplest type of wave is the one in which the
particles of the medium are set into simple
harmonic vibrations as the wave passes through
it. The wave is then called a simple harmonic
wave.
Consider a particle O in the medium. The
displacement at any instant of time is given by

13. Where A is the amplitude, w is the angular frequency
of the wave. Consider a particle P at a distance x from
the particle O on its right. Let the wave travel with a
velocity v from left to right. Since it takes some time
for the disturbance to reach P, its displacement can
be written as

14. Where f is the phase difference between the particles O and P.
We know that a path difference of l corresponds to a phase difference
of 2p radians. Hence a path difference of x corresponds to a phase
difference of 2π x
ʎ
Substituting equation (1.5) in equation (1.4)
We get,

15. Similarly, for a particle at a distance x to the left of 0, the equation for the
displacement is given by

16. 16
Boundary Behavior
• The behavior of a wave when it reaches the
end of its medium is called the wave’s
BOUNDARY BEHAVIOR.
• When one medium ends and another begins,
that is called a boundary.

17. 17
Fixed End
• One type of boundary that a wave may
encounter is that it may be attached to a fixed
end.
• In this case, the end of the medium will not be
able to move.
• What is going to happen if a wave pulse goes
down this string and encounters the fixed
end?

18. 18
Fixed End
• Here the incident pulse is an upward pulse.
• The reflected pulse is upside-down. It is
inverted.
• The reflected pulse has the same speed,
wavelength, and amplitude as the incident
pulse.

19. 19
Fixed End Animation

20. 20
Free End
• Another boundary type is when a wave’s
medium is attached to a stationary object as a
free end.
• In this situation, the end of the medium is
allowed to slide up and down.
• What would happen in this case?

21. 21
Free End
• Here the reflected pulse is not inverted.
• It is identical to the incident pulse, except it is
moving in the opposite direction.
• The speed, wavelength, and amplitude are the
same as the incident pulse.

22. 22
Free End Animation

23. 23
Change in Medium
• Our third boundary condition is when the
medium of a wave changes.
• Think of a thin rope attached to a thin rope.
The point where the two ropes are attached is
the boundary.
• At this point, a wave pulse will transfer from
one medium to another.
• What will happen here?

24. 24
Change in Medium
• In this situation part of the wave is reflected,
and part of the wave is transmitted.
• Part of the wave energy is transferred to the
more dense medium, and part is reflected.
• The transmitted pulse is upright, while the
reflected pulse is inverted.

25. 25
Change in Medium
• The speed and wavelength of the
reflected wave remain the same, but the
amplitude decreases.
• The speed, wavelength, and amplitude of
the transmitted pulse are all smaller than
in the incident pulse.

26. 26
Change in Medium Animation

27. 27
Wave Interaction
• All we have left to discover is how waves
interact with each other.
• When two waves meet while traveling along
the same medium it is called INTERFERENCE.

28. 28
Constructive Interference
• Let’s consider two waves moving towards
each other, both having a positive upward
amplitude.
• What will happen when they meet?

29. 29
Constructive Interference
• They will ADD together to produce a
greater amplitude.
• This is known as CONSTRUCTIVE
INTERFERENCE.

30. 30
Destructive Interference
• Now let’s consider the opposite, two waves
moving towards each other, one having a
positive (upward) and one a negative
(downward) amplitude.
• What will happen when they meet?

31. 31
Destructive Interference
• This time when they add together they
will produce a smaller amplitude.
• This is know as DESTRUCTIVE
INTERFERENCE.

32. 32
Check Your Understanding
• Which points will produce constructive interference
and which will produce destructive interference?
 Constructive
 G, J, M, N
 Destructive
 H, I, K, L, O

33. Quickne tube Experiment