1.5 Analysing Interference of Waves

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WAVES

• 1.5 Analysing Interference of Waves

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LEARNING OUTCOMES

• At the end of the lesson, student is able to
• State the principle of superposition
• Explain the interference o waves
• Draw and interpret interference patterns
• Solve problems using

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• Principle of superposition
• When two or more waves pass through each other,
  the net displacement at a given point is equal to
  the vector sum of the displacement of the
  individual waves.

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• Interference is a phenomenon in which waves from
  two coherent sources passing the same point
  reinforce or cancel each other.
• Coherent sources are sources that produce waves
  having
• The same frequency
• A constant phase difference.
• There are two types of interference, namely
  constructive interference and destructive
  interference.
• Constructive interference occurs when a crest
  meets another crest or a trough meets another
  trough.
• Destructive interference occurs when a crest
  meets a trough.

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INTERFERENCE OF WATER WAVES
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• Along line A1, bright spots are found alternating
  with dark spots.
• At a bright spot, two crests superimpose
  constructively to produce a higher crest.
• At a dark spot, two trough superimpose
  constructively to produce a deeper trough.
• Line A1 is called an antinodal line. Constructive
  interference occurs along an antinodal line.

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• Along line N1, uniform colour is observed. The
  water is calm along line N1
• Crests superimpose with trough, thus destructive
  interference occur.
• Line N1 is called an nodal line.

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• x distance between two successive antinodal
  lines(or nodal lines)
• a distance between the two coherent sources of
  waves
• D distance from each source of waves to line PQ
  where x is measured

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EXERCISE

• Two coherant waves are produced in a ripple tank
  by dippers that are placed 5.0 cm from each
  other. At a distance of 20.0 cm from the dippers,
  the separation between adjacent antinodal lines
  is 3.0 cm. calculate the wavelength of the waves.
  
• ANSWER 0.75 cm

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INTERFERENCE OF SOUND WAVES
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• (a) a loud sound is detected at the position
  where the sound waves from the loudspeakers
  interfere constructively.
• (b) a soft sound is detected at the position
  where the waves from the loudspeakers interfere
  destructively.
• For interference of sound waves, the equation is
  given also as

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EXERCISE

• Two loudspeakers connected to an audio signal
  generator were placed 1.2 m from each other. A
  student who was walking along a line 3.0 m in
  front of the loudspeakers could hear alternating
  loud and soft sounds, the distance between
  adjacent loud and soft sounds is 0.85 m. What is
  the wavelength of the sound.
• ANSWER 0.68 m

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INTERFERENCE OF LIGHT WAVES
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• Interference of light waves can be studied using
  Youngs double slit.
• When a beam of monochromatic light passes through
  the double slit, interference of light produces a
  pattern consisting of bright and dark fringes on
  the screen.

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• The light that passes through each slit is
  diffracted. The two diffracted beams of light
  superimpose.
• (a) at the bright fringe, the light waves from
  each slit interfere constructively.
• (b) at the dark fringe, the light waves from
  each slit interfere destructively.
• For interference of sound waves, the equation is
  given also as

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EXERCISE

• The figure below shows the interference pattern
  formed by red laser light.
• Calculate the value of y.
• ANSWER 8.16 mm