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Name : Teacher: Cheng Wui LeapSubject : SPM Physics Class : F5 Physics Chapter : Waves Lesson No : 4Topic : 1.5 Interference of Waves Date : 28/1/16

Time : 5.15pm-7.15pm

1.5 Interference of Waves

Principle of Superposition 1 The Principle of superposition states that at any instant, the wave displacement of the

combined motion of any number of interacting waves at a point is the sum of the displacements of all the component waves at that point.

2. Figures 1.44 (a), (b) and (c) show the combined amplitude produced when two waves, both of amplitude a, from opposite directions meet.

3. Interference pattern is a result of the superposition of waves.

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Interference of Waves 1. Interference is the superposition of two waves originating from two coherent sources. Sources

which are coherent produce waves of the same frequency (f), amplitude (a) and in phase.2. The superposition of two waves emitted from coherent sources gives either constructive or

destructive interference.3. Constructive interference occurs when the crests or troughs of both waves coincide to

produce a wave with crests and troughs of maximum amplitude.4. Destructive interference occurs when the crest of one wave coincides with the trough of the

other wave, thus cancelling each other with the result that the resultant amplitude is zero.5. Figure 1.45 shows the occurrence of constructive interference and destructive interference.

6. An antinode is a point where constructive interference occurs, whereas a node is a point where destructive interference occurs. From Figure 1.46, it can be seen that the antinode line joins all anti nodes while the node line joins all nodes.

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Exercise 1.

From the points labelled in the above diagram, list the nodes and the antinodes.2. [Q34/P1/SPM’05]The diagram shows the wave pattern formed by waves from two coherent sources,

X and Y.

Destructive interference occurs atA R only B Q only C P and Q

D P and R 3. [Q33/P1/SPM’06]Diagram 20 shows the interference patterns for water waves from two coherent sources, S1 and S2.

Which of the following shows the superposition of the waves at point Y?

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4. [Q32/P1/SPM’08]In which diagram will destructive interference occur when the waves meet?

5. [Q32/P1/SPM’09]Diagram 18 shows two coherent waves propagate towards each other..

Which diagram is correct when both waves meet?

6. [Q31/P1/SPM’10]Diagram 25 shows an interference pattern of water waves from two sources, S1 and S2.

Which form of wave happens at point X from sources S1 and S2?

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7. [Q30/P1/SPM’11]Diagram 21 shows two wave pulses produced at P and Q.P and Q are at the same distance from X.

Which waveform is observed at X?

8. [Q31/P1/SPM’11]Diagram 22 shows an interference pattern produced by two coherent sources in a ripple tank. X, Y and Z are three points located in the interference pattern.

Which combination is correct?

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Notes:-Relationship between , a, x and D

Keys:a = distance between two coherent sources

= wavelengthx = distance between two consecutive node ( or antinode) linesD = distance from the two sources to the point of measurement of xFrom the interference pattern and the factors that influence the interference pattern inexperiment , we found that

and

Combining the two relationships:

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Interference of waves

Type of wave

Water wave Sound wave Light wave

Diagram

Wavelength,

The wavelength of waterwaves is influenced by thefrequency of the vibrator.

The wavelength of soundwaves is influenced by thefrequency of the audio signal generator.

The wavelength of light dependson its colour.

D Distance between thespherical dippers and theposition marked x ismeasured

Distance between the plane of the two loudspeakers and the path along which interference can be detected

Distance between thedouble-slit plate and the screen

a Distance between the twospherical dippers

Distance between the twoLoudspeakers

Distance between the two slits on the double-slit plate

x Distance between twoconsecutive anti node linesor two consecutive node lines

Distance between twoconsecutive positions where a loud sound is heard

Distance between twoconsecutive bright fringes ordark fringes

ExampleIn a Young's double slit experiment to determine the wavelength of light waves, a sodium lamp is used. The separation between the slits of the Young's double slit is 0.5 mm and the distance between the screen and slits is 3.0 m. The separation between two consecutive bright fringes is 3.5 mm. What is the wavelength of the yellow light produced by the sodium lamp?

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Exercise1. Diagram 1 shows the fringe pattern that is produced in a Young's double slit experiment. The

separation between the slits is 0.4 mm and the distance from the slit to the screen is 2.0 m. Calculate the wavelength of the light used in the experiment.

2. A monochromatic light of wavelength 7.0 x 10-5 cm is used in a Young's double slitexperiment. Diagram 2 shows fringes that are produced on the screen due to interference. If the separation between the slits is 0.5 mm, how far is the screen from the double slit?

3. In a Young's double slit experiment, when a red light of wavelength 6.4 x 10-7 m is used as coherent sources, the distance of separation between consecutive fringes is 0.40 mm. If the red light is changed to green light which has a wavelength of 5.2 x10-7m, what is the new distance of separation between the fringes?

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4. A monochromatic light of wavelength 5.0 x 10-5 cm is passing through a double slit. A fringe pattern is formed on a screen which is placed 3 m away from the screen. If the distance between two consecutive dark fringes is 1.5 mm, what is the separation between the slits of the double slit?

5. Diagram 2 shows the experiment set-up of a Young's double slit experiment. Using the measurements shown in the diagram, determine the separation between the slits, a, if the monochromatic light used has a wavelength of 640 nm.

6. In a Young's double slit experiment, when red light and blue light are used as light sources, the fringe pattern formed is as shown in Diagram 3.

Given that the third order of the fringe pattern of red light coincides with the fourth order of the fringe pattern of blue light, what is the ratio of wavelength of red light to the wavelength of blue light?

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7. The diagram below snows the interference pattern produced by two sources of water waves, S1 and S2.

Calculate the wavelength of the water wave using the measurements in the diagram.

8. In a Young's double-slit experiment, the slits are 0.2 mm apart and the screen is 3.5 m away from the slits. If the distance between five consecutive bright fringes is 2.4 cm, what is the wavelength of the monochromatic light?

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[SBP 2009 P2]

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12

[SBP 2011]

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14

[MRSM 2008 P2]

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16

17

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