Periodic Motion and Waves

CHAPTER 13
Waves

© 2013 Marshall Cavendish International (Singapore) Private Limited

13.1 Introducing Waves

13.2 Properties of Wave Motion

Chapter 13 Waves

Learning Outcomes

At the end of this section, you should be able to:
• describe wave motion using vibrations in ropes

and springs, or waves in a ripple tank;

• show an understanding that waves transfer energy

without the transfer of matter;

• state the differences and similarities between a

transverse wave and a longitudinal wave, and
provide appropriate examples of each.

13.1 Introducing Waves

What is a Wave?

• A wave is a disturbance that transfers energy from

one place to another.

• It is made up of periodic motion.

– Periodic motion is motion

repeated at regular intervals.

– The swinging motion of a

pendulum is periodic.

– It moves from A to B, and back

to A at regular intervals.

– When it moves from A to B and

back to A, it completes an
oscillation.

13.1 Introducing Waves

Multiple Choice

A wave transfers

• molecules

• energy

• force

• matter

Waves in a Rope

•Kinetic energy from the moving
hand is transferred to the rope.

•This forms a rope wave (a wave
that travels within the rope).

•The rope wave moves from the
hand to the wall (left to right).

•As the wave moves through the
rope, from left to right, the rope
particles (P and Q) move up
and down, about their rest
positions.

•Eventually, the kinetic energy is
transferred from the hand to the
wall.

13.1 Introducing Waves

Waves in a Ripple Tank

•Kinetic energy from the dipper
is transferred to the water.

•This forms a water wave (i.e. a
water ripple).

•The water wave moves
outwards from the dipper.

•In other words, the kinetic
energy gets transferred from
the dipper to the edges of the
ripple tank.

•The water particles move up
and down, about their rest
positions.

13.1 Introducing Waves

In summary,

• The source of a wave is a vibration or an

oscillation.

• Waves transfer energy from one point to

another.

• Waves transfer energy without transferring

the medium.

13.1 Introducing Waves

Waves in a Spring

If we move the spring in a left-to-right motion…

(top view)

we will observe that the individual spring coils move
perpendicular to the direction of the wave.

13.1 Introducing Waves

Waves in a Spring

If we move the spring in a push-and-pull motion…

we will observe that the individual spring coils move
parallel to the direction of the wave.

13.1 Introducing Waves

Types of Wave Motion

As was seen with the slinky spring, there are two
types of waves:
• Transverse waves
• Longitudinal waves

How do transverse waves differ

from longitudinal waves?

13.1 Introducing Waves

Transverse Waves

•The coils move up and down,
while the wave moves from
left to right.

•The movement of the coils is
perpendicular to the wave
motion.

Transverse waves are waves
that travel perpendicular to
the direction of the medium’s
particle vibration.

13.1 Introducing Waves

Longitudinal Waves

•The coils move left and right,
while the wave moves from
left to right.

•The movement of the coils is
parallel to the wave motion.

Longitudinal waves are
waves that travel parallel to
the direction of the medium’s
particle vibration.

13.1 Introducing Waves

Multiple Choice

Which of the following shows an example each of transverse and longitudinal waves?

• transverse: X-ray

  longitudinal: sound wave

• transverse: sound wave

  longitudinal: X-ray

• transverse: x-ray

  longitudinal: sound wave

• transverse: radiowave

  longitudinal: microwave

13.1 Introducing Waves

13.2 Properties of Wave Motion

Chapter 13 Waves

Learning Outcomes

At the end of this section, you should be able to:

• define, with reference to waves, the terms

speed, frequency, wavelength, period, amplitude
and wavefront;

• recall and apply the relationship

velocity = frequency × wavelength to solve
related problems.

13.2 Properties of Wave Motion

Describing Waves

Crests
The highest points of a transverse wave

Troughs
The lowest points of a transverse wave

P

Q

R

S

T

U

V

Which points on the
wave are crests
and which points
are troughs?

Question

13.2 Properties of Wave Motion

P

Q

R

S

T

U

V

Describing Waves

The amplitude Aof a wave is the maximum possible
displacement of a point from its rest position.

amplitude
(height of crest)

amplitude
(depth of trough)

13.2 Properties of Wave Motion

Multiple Choice

The depth of a water wave is plotted against its position. What is the amplitude of the wave?

• 5 m

• 10 m

• 70 m

• 80 m

Describing Waves

Points along a wave are in phase if they have the same
•direction;

•speed;

•displacement from their rest positions.

P

Q

R

S

T

U

13.2 Properties of Wave Motion

V

Multiple Choice

The following graph shows an instance of a transverse wave moving to the right. Which point is in phase with P?

• A

• B

• C

• D

P

Q

R

S

T

U

V

Describing Waves

The wavelength λ of a wave is the shortest distance
between any two points in phase.

wavelength

wavelength

wavelength

13.2 Properties of Wave Motion

The transverse rope wave can be represented using a
displacement–distance graph.

Displacement–distance Graph

•The blue dots represent the
ribbons P, Q, R, S, T, U and V.

•The arrows show the direction of
motion of the rope at Q and T.

P

Q

R

S

T

U

V

13.2 Properties of Wave Motion

Displacement–distance Graph

•A displacement–time graph describes the displacements of
all the particles at a particular point in time.

•Points above the rest positions are shown as positive
displacements.

•Points below the rest positions are shown as negative
displacements.

13.2 Properties of Wave Motion

Displacement–time Graph

P

Q

R

S

T

U

V

The transverse rope wave can also be represented
using a displacement–time graph.

We do this by tracking the displacement of one
particle, say ribbon Q, over a period of time.

13.2 Properties of Wave Motion

Displacement–time Graph

Using the information gathered, we
can then plot the displacement of
ribbon Q over a period of time.

UR
L

13.2 Properties of Wave Motion

Describing Waves

The period Tof a wave is the time taken to
produce one complete wave.

The frequency fof a wave is the number of
complete waves produced per second.

The SI unit of period is the second (s).

The SI unit of frequency is the hertz (Hz).

f = 1

T

13.2 Properties of Wave Motion

Describing Waves

Wave speed vis the distance travelled by a
wave per second.

The SI unit of wave speed is the metre per second
(m s–1).

Since a point on a wave travels a distance of one
wavelength in one period, wave speed is given by:

v = λ

T

v = fλ

13.2 Properties of Wave Motion

Multiple Choice

A student moves his hand to create a rope wave with a wavelength of 20 cm. The student then doubles the frequency at which his hand oscillates. What will be the new wavelength of the rope, assuming that the speed of the wave remains constant?

• 10 cm

• 20 cm

• 40 cm

• 80 cm

Describing Waves

A wavefront is an imaginary line on a wave
that joins all adjacent points that are in phase.

A straight dipper produces plane
wavefronts, while a spherical dipper
produces circular wavefronts.

13.2 Properties of Wave Motion

Multiple Choice

The scale diagram shows the wave pattern produced by a straight dipper in a ripple tank. The equally spaced lines represent the wavefronts. What is the wavelength of each wave?

• 1 cm

• 2 cm

• 3 cm

• 4 cm

Worked Example

A wave in a string is travelling to the right at 2 m s–1.
The diagram below shows its displacement–distance
graph at t = 0 s.

(a) Sketch the graph to show how the wave will

appear at t = 3 s.

(b) Draw and label the position of P and Q at t = 3 s.

Displacement/m

Distance/m

P

8

2

4

6

Q

13.2 Properties of Wave Motion

Solution

x/m

d/m
P
t = 3 s

x/m

d/m

P

8

2

4

6

Q

Q

t = 0 s

13.2 Properties of Wave Motion

Multiple Choice

It takes 0.50 s to generate one complete wave in a ripple tank. The speed of the wave is 5 cm/s. What is the wavelength of the wave?

• 0.1 cm

• 2.5 cm

• 10 cm

• 250 cm

Worked Example

A transverse wave is travelling to the right at 2 m s–1.
The diagram below is its displacement–distance graph
at t = 0 s.

Plot a graph to show how the displacements of
particles P and Q vary with time.

Displacement/m

Distance/m

P

8

2

4

6

Q

13.2 Properties of Wave Motion

Solution

Displacement/m
P

Time/s

Q

4

2

1

3

13.2 Properties of Wave Motion

Multiple Choice

The depth of a water wave travelling with a speed of 3 m/s is plotted against time. What is the wavelength of the water wave?

• 1 m

• 2 m

• 4 m

• 12 m

Wave

s

Types of
waves

Chapter 13 Waves

Characteristics

Quantities/Terms

Graphs

•Transverse

•Longitudina
l

•Transfer
energy

•Do not
transfer
matter

•Amplitude (A)

•Wavelength (λ)

•Period (T)

•Frequency (f)

•Wave speed 

(v = fλ)

•Wavefront

•Displacement–
distance graph

•Displacement–
time graph