Unit One: Periodic Motion
There are two types of motion—transitional and periodic. Periodic motion is motion which is regularly repeated
in equal periods of time. Oscillatory motion and wave motion are examples of periodic motion.
Lesson one: Oscillatory Motion
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Concept of oscillatory motion
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Graphical representation of oscillatory motion
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Properties of oscillatory motion
o Amplitude
o Oscillation
o Periodic time
o Frequency
1. Concept of oscillatory motion
Oscillatory motion is the periodic motion of an oscillating object around its equilibrium position, where the
motion is repeated through equal intervals of time.
𝑚𝑣 2
The kinetic energy of an oscillating object can be found using the following formula: 𝐾𝐸 = 2 , which can
also be written as 𝐾𝐸 = 1⁄2 𝑚𝑣 2 . So, assuming that the mass of the object does not change, its kinetic
energy increases as its velocity increases. Specifically, the kinetic energy of an object increases by a factor
proportional to the square of the velocity increase. For example, still assuming the mass remains unchanged,
when the velocity doubles, the kinetic energy quadruples (it increases by a factor of 4, which is the square
of the factor of which the velocity increases)
The velocity and kinetic energy of an object reach their peak at the equilibrium point, and they reach zero
when they are at the maximum displacement points. That indicates that the velocity of the oscillating body
is inversely proportional to its displacement away from its equilibrium point.
Examples of oscillatory motion:
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Pendulum
Tuning fork
Spring
Stretched string
Swing
Graphical representation of oscillatory motion
On a two-dimensional plane where the x-axis represents time and the y-axis
represents displacement, the relation between the velocity and displacement can
be represented by the following graph.
2. Properties of oscillatory motion
2.1.
Amplitude
The amplitude in oscillatory motion is the maximum displacement achieved
by the oscillating body away from its equilibrium point. It is equal to one quarter of a complete
oscillation.
2.2.
Complete oscillation
A complete oscillation is the motion of an oscillating body when it passes through a fixed point on its
path twice in the same direction.
2.3.
Periodic time
In oscillatory motion, the periodic time (𝑇) is the time taken by an oscillating body to complete one
complete oscillation.
2.4.
Frequency
In oscillatory motion, the frequency (𝐹) is the number of complete oscillations completed by an
oscillating object per unit time. One oscillation per second is equal to one hertz (1 Hz).
Other Laws
𝑡
𝑇 = 𝑜 where 𝑡 is the time and 𝑜 is the number of complete oscillations.
𝑜
𝐹 = 𝑡.
From those two relations, it is concluded that 𝑇 and 𝐹 are inversely proportional. So,
𝑇 = 𝐹 −1 , 𝐹 = 𝑇 −1 .
When an oscillating object completes one oscillation in one second, the frequency and periodic time are equal.
Lesson two: Wave Motion
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Role of waves in transferring energy
Concept of wave motion
Types of waves
Properties of wave motion
o Wavelength
o Amplitude
o Velocity
o Frequency
1. Role of waves in transferring energy
A wave is the disturbance that propagates and transfers energy in the direction of propagation. An example
of this is when one domino piece falls, transferring its energy to all the dominoes in its falling direction (the
direction of propagation).
2. Concept of wave motion
Wave motion is the periodic motion achieved as a result of the vibration of medium particles at a certain
point in time and direction.
The line of wave propagation is the direction of the progression of the wave.
3. Types of waves
Waves can be classified based on:
 The direction of vibration of medium particles relative to the direction of wave propagation
into
o Transverse waves
o Longitudinal waves, and based on
 The ability of the wave to propagate and transfer energy
into
o Electromagnetic waves
o Mechanical waves.
The transverse wave is a wave in which the medium particles vibrate perpendicular to the direction of
propagation. The longitudinal wave is a wave in which the medium particles vibrate along the direction of
propagation. A transverse wave forms crests and troughs, and a longitudinal wave forms compressions and
rarefactions.
The crest is the highest point of the medium particles in the transverse, and the trough is the lowest.
Similarly, the compression is the area in the longitudinal wave at which the medium particles are at the
highest density and pressure, and the rarefaction is the area at which they are at the lowest density and
pressure.
In the wave motion curve, the crest and trough points of the transverse wave are equivalent to the centre
of compression and the centre of rarefaction in the longitudinal wave respectively.
Electromagnetic waves are waves which do not need a medium to propagate, meaning that they can
propagate through vacuum. They are all transverse waves, and they travel through vacuum at the speed of
light (299 792 458 m/s), and their velocity decreases when they travel through media. Examples of
electromagnetic waves include visible light, infrared, and radio waves.
Mechanical waves are waves which need a medium to propagate. They may be transverse waves, such as
water waves, or longitudinal waves, such as sound waves. Their speed varies widely, but they are all much
slower than electromagnetic waves.
4. Properties of wave motion
4.1.
Wavelength
The wavelength (𝜆) of the transverse wave is the distance between two successive crests or toughs. The
wavelength of the longitudinal wave is the distance between two successive compressions or
rarefactions. The wavelength of a wave can be found using the three following laws:
i.
In a transverse wave, 𝜆 = twice the horizontal distance between the successive crest and trough.
ii.
In a longitudinal wave, 𝜆 = twice the distance between the centres of the successive
compression and rarefaction.
iii.
𝑑
𝜆 = 𝑛 where 𝑑 is the distance covered by waves, and 𝑛 is the number of waves.
4.2.
Wave amplitude
The wave amplitude is the maximum displacement achieved by the medium particles away from their
equilibrium points. It is equal to half the vertical distance between the successive crest and trough of a
curve.
4.3.
Wave velocity
The wave velocity is the distance covered by the wave per unit time.
4.4.
Wave frequency and periodic time
The wave frequency is the number of complete waves produced from the source per unit time. It is
measured in Hertz, where one wave per second is equivalent to 1 Hz. As with oscillatory motion, its
inverse is the periodic time of the wave, defined as the time taken to produce one wave.
The law of wave propagation states that the velocity of the wave in m/s is equal to the product of the
frequency in Hertz and the wavelength in metres. Thus, 𝑣 = 𝐹𝜆. From this law, it is concluded that:
𝑣
𝑣
i.
𝐹 = 𝜆 and 𝜆 = 𝐹, therefore the frequency and wavelength of a wave are inversely proportional
ii.
iii.
iv.
at constant velocity
The velocity of a wave is directly proportional to its frequency at constant wavelength
The velocity of a wave is directly proportional to its wavelength at constant velocity.
The frequency and periodic time of a wave are equal when the source produces one complete
wave in one second.