Wave Properties Harmonic Motion and Mechanical Waves The law of reflection the angle of incidence equals the angle of reflection. The normal is an imaginary line that is perpendicular to the surface. The angle of incidence is always measured between the incident ray and the normal, while the angle of reflection is measured between the reflected ray and the normal. 1
Law of Reflection Jun 5 7:55 AM 2
Interference and Superposition Points 1. Understand what happens when two waves occupy the same space. 2. Learn the two types of interference. 3. Understand how this can be applied to practical uses. Jun 5 8:08 AM The Principle of Linear Superposition and Interference Phenomena There is a straightforward way to deal with situations in which two or more waves pass through the same place simultaneously. The diagrams at right show what happens when waves interfere with each other. Jun 5 8:09 AM 3
Superposition When two or more waves exist in a medium, they will combine algebraically to produce a resultant wave. Jun 5 8:10 AM Constructive Interference When a crest meets a crest or a trough meets a trough, they combine and the energies combine and work together. This "meeting" will produce a maximum disturbance which can be termed an anti - nodal line. Jun 5 8:11 AM 4
Destructive Interference When a crest meets a trough, they cancel each other out because the energy of the crest and trough work against each other. This "meeting" will produce a minimum disturbance which can be termed a nodal line. Jun 5 8:07 AM Jun 5 7:57 AM 5
Principle of Linear Superposition When two or more waves are present simultaneously at the same place, the resultant wave is the sum of the individual waves. In both cases, Constructive and Destructive Interference, the crest and troughs pass through each other only producing an interference pattern when they meet. Example 1 : Calculate the amplitude of the combined wave when the following amplitudes combine in phase and out of phase. 4.5 cm and 3.6 cm 6
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Interference In general, the important issue is the difference in the distances traveled by each wave when overlapping. A difference that is an integer (1,2,3 ) number of wavelengths gives constructive interference while half integer (1.5,2.5,3.5 ) number of wavelengths gives destructive interference. Eg) Two loudspeakers, A and B, are separated by 3.20m. A listener is stationed at point C, which is 2.40m directly in front of speaker B. The triangle ABC is a right triangle. Both speakers are playing identical 214Hz tones, and the speed of sound is 343m/s. Does the listener hear a loud sound or no sound? 2.4m 3.2m Using Pythagorean theorem to find the length of AC since BC is 2.40m. The difference in distances traveled between the two waves is. So the listener will hear a loud sound if the wavelength of the sound is any factor of 1.60m and no sound if it is half a wavelength out of phase. Jun 5 8:01 AM 8
Standing Waves Exist when the wave pattern does not move. Usually this will occur when the wave medium is attached at both ends. These waves have alternating nodes and anti - nodes. The distance between nodes or between anti - nodes is half of a wavelength (0.5λ) These can be produced when the reflecting wave interferes with the incident wave in an air column Standing Waves Read and Make notes On p. 416 420 Do p. 420 #1, 2 Jun 5 8:05 AM 9
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