Chapter 3: Waves
3.1 Understanding Waves
Motion of Waves
• 1 An oscillating or vibrating motion in
which a point or body moves back and
forth along a line about a fixed central
point produces waves.
Motion of Waves
• 2. Examples of waves:
• (a) Light waves are produced as a
result of vibrations of electrons in an
atom.
Motion of Waves
• 2. Examples of waves:
• (b)Sound waves are produced by
vibrating mechanical bodies such as
guitar strings or a tuning fork.
Motion of Waves
• 2. Examples of waves:
• (c) Water waves are produced by
disturbance (or vibration) on a still
water surface.
Propagation (Traveling) of
Waves
• 1.When a wave travels through a
medium, the particles of the medium
vibrate about their equilibrium
positions.
Direction of
waves
Propagation (Traveling) of
Waves
• 2. However, the particles of the
medium do not travel in the
direction of the wave.
• 3. A wave transfers energy and
the momentum from the source
of the wave (the oscillating or
vibrating system) to the
surroundings.
Wave fronts
• 1. A wave front is a line or plane on
which the vibrations of every points
on it are in phase and are at the
same distance from the source of the
wave.
Same
Phase
Wave fronts
• 2 . Points in a wave are in phase if
they vibrate in the same direction
with the same displacement.
Same
displacement
Plane Wave fronts
• 1 . Figure 1.3 shows the production of
plane water waves when a wooden
bar vibrates vertically at a constant
frequency on the surface of the water.
Plane Wave fronts
• 2. Lines PQ, RS, TU and VW are straight
lines along the respective crests of the
waves. These lines are called wave
fronts.
Circular Wave fronts
• 1. When we use a fingertip to touch
the surface of water repeatedly,
circular wave fronts are produced as
shown in Figure 1.4.
Types of Waves
• There are two types of waves.
• (a) Transverse wave
• (b) Longitudinal wave
Transverse Waves
• 1. A transverse wave is a wave in
which the vibration of particles in the
medium is at right angle
(perpendicular) to the direction of
propagation of the wave.
Transverse Waves
• 2. A model of a transverse wave can
be produced by a slinky spring as
shown in Figure 1.6.
Transverse Waves
• 3. Examples of transverse waves are
water waves and electromagnetic
waves.
Longitudinal Waves
• 1. A longitudinal wave is a wave in
which the vibration of particles in the
medium is parallel to the direction of
propagation of the wave.
Longitudinal Waves
• 2. When the slinky spring is vibrated
back and forth along the direction of
propagation of the wave at a fixed
rate, a longitudinal wave is produced
as shown in Figure 1.8.
Longitudinal Waves
• 3 . Example of longitudinal waves is
sound waves.
Amplitude, Period and Frequency of a
Wave
• 1 . The amplitude, A, of a vibrating system is
maximum displacement from its equilibrium
position. It is a measure of height of the wave crest
or depth of the wave trough.
Amplitude
Amplitude, Period and Frequency of a
Wave
• 2 . In Figures 1.9 (a) and (b), the distance OQ is the
amplitude, where O is the equilibrium position of
the vibrating system.
Amplitude
Amplitude, Period and Frequency of a
Wave
• 3 . The period, T, of a vibrating system is the time
taken to complete an oscillation.
Period
Amplitude, Period and Frequency of a
Wave
• 5. If a vibrating system makes n
complete oscillations in a time of t
seconds, the period of oscillation, T of
the system is
• The SI unit of period is second.
Amplitude, Period and
Frequency of a Wave
• 6. The frequency, f, is the number of
complete oscillations made by a vibrating
system in one second.
• The unit of frequency is hertz (Hz) or s-1.
Amplitude, Period and
Frequency of a Wave
• 7 From the formulae of T and f, the relationship
between period, T and frequency, f is:
• T is inversely proportional to f and vice versa.
Amplitude, Period and
Frequency of a Wave
• Example 1:
• In an experiment, Aziz observes that a simple
pendulum completes 30 oscillations in 48.0 seconds.
What is
• (a) the period of oscillation?
• (b) the frequency of oscillation?
Amplitude, Period and
Frequency of a Wave
• Example 1:
• Solution
• (a) Period, T time taken
number of completed oscillation
48.0
1.6s
30
Amplitude, Period and
Frequency of a Wave
• Example 1:
• Solution
• (b)
1
frequency,f 1
0.625Hz
T 1.6
Displacement-time Graph of a
Wave
• 1. The sinusoidal graph in Figure 1.10 is
a graph of displacement, s against
time, t of a load on a spring.
Displacement-time Graph of a
Wave
• 2 From the graph of s against t in Figure 1.10, the
following information is obtained.
• (a) Amplitude, A = a cm
• (b) Period of oscillation, T is the time between
points:
• (i) O and F, (ii) C and G or (iii) P and Q.
Displacement-time Graph of a
Wave
• Example 2:
• Figure 1.11 shows the displacement-time graph of
the oscillation of a mass on a spring.
• (a) state the amplitude,
• (b) calculate the period of the oscillation,
• (c) calculate the frequency of the oscillation
Displacement-time Graph of a
Wave
• Example 2:
• Solution
• (a) Amplitude, A = 5 cm
•
• Example 2:
• Solution
• (b) Period of oscillation, T = 0.04 s
• Example 2:
• Solution
• (c) Frequency of oscillation,
1 1
f 25Hz
T 0.04
Displacement-distance Graph
of a Wave
• 1. Figures 1.12 (a) and (b) show the
propagation of a water wave and a
sound wave.
Displacement-distance Graph
of a Wave
R: Rarefaction
C:Compression
Displacement-distance Graph
of a Wave
• 2. The displacement, s of each particle of the
medium at different distances can be shown in a
displacement-distance graph as shown in Figure
1.12 (c).
Displacement-distance Graph
of a Wave
• 3. The wavelength is the distance
between successive points of the same
phase in a wave.
Displacement-distance Graph
of a Wave
• (b) the distance between two successive
compressions or two successive rarefactions in
a sound wave.
The SI unit of wavelength is metre (m).
Displacement-distance Graph
of a Wave
• Example 3:
• Figure 1.13 shows a displacement-distance
graph of a wave.
• Find
• (a) the amplitude,
• (b) the wavelength of the wave.
Relationship between Speed (v),
wavelength ,and Frequency
(f)
• Wave equation
Relationship between Speed (v),
wavelength , and Frequency
(f)
• Example 4:
• A wave of frequency 120 Hz has a
wavelength of 5.0 m. What is the
speed of the wave?
Relationship between Speed (v),
wavelength ,and Frequency
(f)
• Example 5:
• The displacement-distance graph in
Figure 1.14 shows the motion of a
transverse wave. The source of the
wave produces 10 complete waves in
one second.
Relationship between Speed (v), wavelength,
and Frequency (f)
• Example 5:
• Calculate
• (a) the amplitude,
• (b) the wavelength, and
• (c) the speed of the wave.
