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SPM Physics

6.1.5 Displacement-Time Graph

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Oscillation

  1. Waves are formed by a series of oscillation.
  2. In order to understand waves, we must understand oscillation.

Technical Terms Related to Oscillation

  1. An equilibrium position is a point where an oscillating object experiences zero resultant forces.
  2. A complete oscillation occurs when the vibrating object:
    1. moves to and fro from its original position and
    2. moves in the same direction as its original motion.



  3. Amplitude is the maximum amplitude of an object from its equilibrium position. The SI unit for amplitude is meter, m.



  4. The greater the amplitude, the greater the mechanical energy possessed by the oscillating system.
  5. Period is defined as the time required for one complete oscillation or vibration .
  6. Frequency, f is the number of oscillation that take place in one second. The SI unit for frequency is Herz (Hz).
  7. Frequency can be related to period by the following equation

    f = frequency
    T = Period


Example:
Given that a pendulum makes 20 oscillations in 25s. Find the frequency of the pendulum.

Answer:
Period,


Frequency



In a displacement-time graph, we can determine
  1. The displacement of the oscillating object at any time.
  2. The amplitude
  3. The period.


Example:

Figure above shows a displacement versus time graph for a vibrating object.
a. Find the amplitude, period and frequency for the vibrating system.
b. What is the displacement of the object at t = 0.3 s,
c. Sketch in the same axis above, a graph of a wave which the frequency and amplitude are half of the wave in the figure above.

Answer:
a.
The amplitude, A = 10cm
The period, T = 0.4s
The frequency,



b. The displacement at 0.3s = -10cm

c.



Comparing Displacement-Time Graph and Displacement- Distance Graph

（Displacement-time graph - Graph of oscillation)

(Displacement-distance graph - Graph of Waves)

  1. Both the displacement-time graph and the displacement distance graph looked similar. However they are 2 different types of graph.
  2. The displacement-time graph illustrate the displacement of an object over time whereas the displacement-distance graph tell the position of the vibrating particles of a wave.
  3. For a displacement- distance graph, the distance between 2 crest/trough represent the period whereas for the displacement-distance graph, it represents the wavelength.

 

6.1.4 Displacement – Distance Graph

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  1. A Displacement – Distance graph shows the position of each particle in a wave relative to its distance from a reference point.
  2. The distance between two (2) successive crest or trough is the wavelength.
  3. The maximum displacement of the particles from the equilibrium position (displacement = 0) is the amplitude.
  4. The amplitude of the wave will increase as the energy transfers by the wave increase and vice versa.


 

6.1.3 Transverse Wave and Longitudinal Wave

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Waves can be classified into 2 groups

  1. transverse wave
  2. longitudinal wave

Transverse Wave

A transverse wave is a wave where the particles of the medium vibrate in a direction that is perpendicular to the direction of the wave motion.

Example:
Light wave, ripple, radio wave

Longitudinal Wave

A longitudinal wave is a wave where the particles of the medium vibrate in a direction that is parallel to the direction of the wave motion.

Example:
Sound Wave

Transverse Wave – Crest and Trough

  1. When discussing wave, it’s important to know what is meant by the crest and trough of a wave.
  2. The point at which the displacement of the water from its normal level is highest called the crest of the wave
  3. The point at which the displacement of the water from its normal level is lowest called the trough of the wave. 

Longitudinal Wave – Compression and Rarefaction

  1. Unlike transverse wave, longitudinal waves have no crest and trough, instead, they have compression and rarefaction.
  2. In compression regions of longitudinal waves, wave particles of the medium are packed closer.
  3. In rarefaction regions, wave particles of the medium are packed further apart.

Finding Wavelength from a Diagram

Transverse Wave


Wavelength is the distance between two successive crest or trough.

Longitudinal Wave


Wavelength is the distance between two successive compression or rarefaction.

Wave front diagram


Wavelength is the distance between two successive wave front

Example 1:

Figure above shows the propagation of a water wave. What is the amplitude of the wave?

Answer:
Amplitude = 10cm/2 = 5cm

Example 2 :

The figure above shows a transverse wave. The wavelength of the wave is equal to
Answer:



Example 3:

The figure above shows the simulation of longitudinal wave by using a slinky spring. What is the wavelength of the wave?
Answer:



Example 4:

The figure above shows the simulation of transverse wave by using a slinky spring. What is the wavelength of the wave?
Answer:



 

6.1.2 Wavefronts

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Phase

  1. A phase is the current position in the cycle of something that changes cyclically.
  2. Two vibrating particles are in the same phase if their displacement and direction of motion are the same.
    1. In phase – Same phase
    2. Out of phase – Different phase
    3. Anti-phase – Phase different = 180°

Wavefront

  1. A wavefront is a line or a surface that connects points that are moving at the same phase and has the same distance from the source of the waves.
  2. When a circular wave is formed, a circular wave front is formed.
  3. Characteristics of wavefront:
    1. wavefronts are always perpendicular to the direction of wave propagation. (As shown in the diagram below)
    2. all the points on a wavefront have same distance from the source of the wave.

Wavelength


The wavelength (λ) is defined as the distance between two successive particles which are at the same phase (exactly the same point in their paths and are moving in the same direction.).


 

6.1.1 Understanding Waves

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What is Wave?

  1. A wave is a disturbance or variation that propagates through a medium, often transferring energy.
  2. Waves travel and transfer energy (its amplitude) and information (its frequency) from one point to another, with little or no permanent displacement of the particles of the medium.
Must Know:
Waves transfer energy without transferring physical matter.

 

 

5.5.6 Slide Projector

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Function

Bulb
  1. Bulb with high brightness is used.
  2. The bulb must be placed at the centre of curvature of the concave mirror.
Concave mirror
  1. The function of the concave mirror is to reflect and focus light that shines on it to the direction of the condenser.
  2. This is to increase the brightness of the image.
Condenser
  1. The condenser consists of two Plano-convex lenses.
  2. The function of the condenser is to focus all the light that brightens the whole slide.
  3. It also acts as a heat insulator to stop heat from the bulb so it does not spoil the slide.
Slide
  1. The slide acts as the object.
  2. It is located at a distance between f and 2f from the projector lens so that the image produced is real and magnified.
  3. It is purposely placed upside down so that the image forms on the screen looks upright.
Projector Lens
  1. The projector lens projects the image on the screen that is placed a few meters away.
  2. It can be adjusted to focus a sharp image.
Image The image produced is
  1. real (it form on a screen)
  2. magnified
  3. inverted (Since the slide is placed upside down, hence the image looks upright)

 

5.5.5 Camera

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Functions

Convex lens To focus the light of an object onto the film so that a sharp image can be produced.
Diaphragm To control the size of the aperture and hence control the amount of light move into the camera.
Focusing Ring To adjust the distance between the lens and the film so that the image is sharply focus on the film.
Film
  1. Acts as a screen for the image to form onto it.
  2. Chemical on it will react when exposed to light and produce a photograph.
Shutter Open when picture is taken to allow light move onto the film.
The shutter speed is the length of time when the shutter is open. It control the amount of light move onto the film.
Aperture Open when picture is taken to allow light move onto the film.
The shutter speed is the length of time when the shutter is open. It control the amount of light move onto the film.

Note:

  1. The film, which is normally kept in total darkness, contains a light-sensitive chemical called silver bromide.
  2. When you press the camera button, a shutter in front of the film opens then shuts again, exposing the film to light for a brief moment only. 
  3. Different intensities and colours of light across the image cause varying chemical changes in the film, which can later be developed, 'fixed', and used in printing a photograph.
  4. The image formed on the film is
    1. Real
    2. Inverted
    3. Smaller than the object.

 

5.5.4 Compound Microscope

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Compound Microscope
Object lens Higher power
Eye lens Lower power
Position of the object The object is placed at a position between fo and 2fo.
Nature of the image, I1 Real, inverted and magnified
Position of the image, I1. The first image, I1 must be placed between the optical center of the eye lens with the eye lens principle focus point, fe.
Nature of the image, I2 Virtual, inverted and magnified
Distance in between the two lens The distance between the object lens and the eye lens in a compound microscope is bigger than the sum of the  focal length (fo + fe).
If the distance between both lenses are adjusted to less than (fo + fe), no image can be seen.
Magnification of the compound  microscope.

m1 = Linear magnification of the object lens
m2 = Linear magnification of the object lens

 

5.5.3 Astronomical Telescope

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Astronomical Telescope
Objective lens Lower power
Eye lens Higher power
Position of the object At infinity
Nature of the image, I1 Real, inverted and magnified
Position of the image, I1. At the principle focus of object lens, fo.
Nature of the image, I2 Virtual, inverted and smaller in size.
Distance in between the two lens
  1. The distance between the object lens and the eye lens in a compound microscope is equal to the sum of the  focal length (fo + fe).
  2. If the distance between both lenses are bigger than (fo + fe), no image can be seen.
Magnification of the compound  microscope.

 

 

5.5.2 Magnifying Glass

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  1. Magnifying glass is also known as simple microscope.
  2. A magnifying glass is a single convex lens with short focal length.
  3. The iage formed is
    1. virtual,
    2. magnified
    3. upright
  4. A magnifying glass enlarges the image of an object by increasing the virtual angle at the eye when the object is viewed.