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TOPIC 1: WAVES | PHYSICS FORM 4

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Introduction to Waves

The Concept of Wave
Explain the concept of a wave
A wave is a disturbance that travels through a medium from one location to another location.
Consider a slinky wave as an example of a wave. When the slinky is stretched from end to end and is held at rest, it assumes a natural position known as the equilibrium or rest position.
The coils of the slinky naturally assume this position, spaced equally far apart. To introduce a wave into the slinky, the first particle is displaced or moved from its equilibrium or rest position. The particle might be moved upwards or downwards, forwards or backwards; but once moved, it is returned to its original equilibrium or rest position.
The act of moving the first coil of the slinky in a given direction and then returning it to its equilibrium position creates a disturbance in the slinky. We can then observe this disturbance moving through the slinky from one end to the other. If the first coil of the slinky is given a single back-and-forth vibration, then we call the observed motion of the disturbance through the slinky a slinky pulse.
pulse is a single disturbance moving through a medium from one location to another location.
However,
if the first coil of the slinky is continuously and periodically
vibrated in a back-and-forth manner, we would observe a repeating
disturbance moving within the slinky that endures over some prolonged
period of time. The repeating and periodic disturbance that moves
through a medium from one location to another is referred to as a wave.
medium is a substance or material that carries the wave.
You have perhaps heard of the phrase news media.
The news media refers to the various institutions (newspaper offices,
television stations, radio stations, etc.) within our society that carry
the news from one location to another. The news moves through the media.
The
wave medium is not the wave and it doesn’t make the wave; it merely
carries or transports the wave from its source to other locations.
In
the case of our slinky wave, the medium through that the wave travels
is the slinky coils. In the case of a water wave in the ocean, the
medium through which the wave travels is the ocean water. In the case of
a sound wave moving from the church choir to the pews, the medium
through which the sound wave travels is the air in the room.
The Terms Wave Length, Frequency and Velocity of a Wave
Explain the terms wave length, frequency and velocity of a wave
Consider the transverse wave below:
  1. transverse
    wave is a wave in which the particles of the medium are displaced in a
    direction perpendicular to the direction of energy transport.
  2. The crest
    of a wave is the point on the medium that exhibits the maximum amount
    of positive or upward displacement from the rest position.
  3. The trough
    of a wave is the point on the medium that exhibits the maximum amount
    of negative or downward displacement from the rest position.
  4. The amplitude
    of a wave refers to the maximum amount of displacement of a particle on
    the medium from its rest position. In a sense, the amplitude is the
    distance from rest to crest. Similarly, the amplitude can be measured from the rest position to the trough position.
  5. The wavelength
    of a wave is simply the length of one complete wave cycle. If you were
    to trace your finger across the wave in the diagram above, you would
    notice that your finger repeats its path. A wave is a repeating pattern.
    It repeats itself in a periodic and regular fashion over both time and
    space. And the length of one such spatial repetition (known as a wave cycle)
    is the wavelength. The wavelength can be measured as the distance from
    crest to crest or from trough to trough. In fact, the wavelength of a
    wave can be measured as the distance from a point on a wave to the
    corresponding point on the next cycle of the wave.
  6. longitudinal
    wave is a wave in which the particles of the medium are displaced in a
    direction parallel to the direction of energy transport. A longitudinal
    wave can be created in a slinky if the slinky is stretched out
    horizontally and the end coil is vibrated back-and-forth in a horizontal
    direction.
  7. compression is a point on a
    medium through which a longitudinal wave is traveling that has the
    maximum density. A region where the coils are spread apart, thus
    maximizing the distance between coils, is known as a rarefaction.
  8. rarefaction
    is a point on a medium through which a longitudinal wave is traveling
    that has the minimum density. Points A, C and E on the diagram above
    represent compressions and points B, D, and F represent rarefactions.
  9. The frequency, (f)
    of a wave refers to how often the particles of the medium vibrate when a
    wave passes through the medium. Given this definition, it is reasonable
    that the quantity frequency would have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is the Hertz
    (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. If a coil
    of slinky makes 2 vibrational cycles in one second, then the frequency
    is 2 Hz.
  10. Period, (T) refers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. The period
    of a wave is the time for a particle on a medium to make one complete
    vibrational cycle. Period, being a time, is measured in units of time
    such as seconds, hours, days or years. The period of orbit for the Earth
    around the Sun is approximately 365 days; it takes 365 days for the
    Earth to complete a cycle.
  11. The speed of an
    object refers to how fast an object is moving and is usually expressed
    as the distance traveled per time of travel. In the case of a wave, the
    speed is the distance traveled by a given point on the wave (such as a
    crest) in a given interval of time.The SI unit of speed is m/s.
Wave equation
The wave equation shows the relationship between speed, wavelength and frequency of a wave.
The
diagrams below show several “snapshots” of the production of a wave
within a rope. The motion of the disturbance along the medium after
every one-fourth of a period is depicted. Observe that in the time it
takes from the first to the last snapshot, the hand has made one
complete back-and-forth motion.
A
period has elapsed. Observe that during this same amount of time, the
leading edge of the disturbance has moved a distance equal to one
complete wavelength. So in a time of one period, the wave has moved a
distance of one wavelength. Combining this information with the equation
for speed (speed = distance/time), it can be said that the speed of a
wave is also the wavelength/period.
Since
the period is the reciprocal of the frequency, the expression 1/f can
be substituted into the above equation for period. Rearranging the
equation yields a new equation of the form:
Speed = Wavelength • Frequency.The above equation is known as the wave equation. It states the mathematical relationship between the speed (v) of a wave and its wavelength (λ) and frequency (f). Using the symbols v, λ, and f, the equation can be rewritten asv = f • λ
Types of Waves
Identify types of waves
Previously
we classified the waves by considering the movement of the particles.
And now you’re going to find out the 2 types of waves according to the
media of propagation.
  1. Mechanical Waves
  2. Electromagnetic Waves
Mechanical Waves
Mechanical
waves are also called elastic waves as their propagation depends on the
elastic properties of the medium through which the waves pass
Mechanical
waves are divided into three categories: Transverse waves, longitudinal
waves, and surface waves. In transverse waves, the medium moves
perpendicular to the wave direction, and in longitudinal waves, the
medium moves parallel to the wave direction.
In
surface waves, both transverse and longitudinal waves mix in a single
medium. In very simple words, an electronic wave is that which travels
in a vacuum, and a mechanical wave is that which needs some medium for
traveling.
Examples of mechanical waves are Sound waves, Water waves , Ocean waves, Earth quake waves, Seismic waves
Electromagnetic Waves
Electromagnetic
waves are waves that have no medium to travel whereas mechanical waves
need a medium for its transmission. Examples of electromagnetic waves
include light and radio signals.
The following are the differences between mechanical and electromagnetic waves.
  • Electromagnetic waves travel in a vacuum whereas mechanical waves do not.
  • The mechanical waves need a medium like water, air, or anything for it to travel.
  • While an electromagnetic wave is called just a disturbance, a mechanical wave is considered a periodic disturbance.

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