8.3: Wave Interactions Flashcards
Wave
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Mechanical waves transfer energy through a medium. A change in the physical characteristics in a medium can be of density and temperature, therefore changing the medium. When the medium ends or changes, the wave does not just stop.
The energy of the wave:
* some energy will be reflected
* some energy will be absorbed by the new medium
* some energy will be transmitted
Solid Boundary End
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- When a transverse wave pulse reached a hard surface (e.g the fixed end of a rope), this pulse is reflected, with almost no energy loss, since the original amplitude is maintained
- The wave however, has been inverted, this can be described as a “reversal in phase”
- Phase change of a wave on reflection from a fixed end can be explained by Newton’s third law: “for every action (force) in nature there is an equal and opposite reaction”.
- When the pulse arrives at the fixed end, the pole exerts an equal and opposite force on the string, thus inverts the wave pulse and sends its reflection back. There is a phase reversal on reflection.
- The phase of the wave has shifted by 1/2λ or λ/2, this inversion can also be 180 degree change of phase
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Free Boundary End
- When a wave pulse hits the end of a rope that is free to move, the pulse returns with no change of phase, there is no reversal in phase
- The crest reflects as a crest, the trough, reflects as a trough
Greater density boundary end
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- When the transverse wave pulse is reflected at a change in medium, some of the amplitude of the reflected wave is absorbed by the post, some is transformed into heat energy, and some continues to travel through the post. The change in density has the same effect as a change in medium
- When a transverse wave pulse is sent from the light rope to the heavy rope, part of the wave pulse will be reflected and part of it will be transmitted to the heavier rope
- Because the second rope is heavier, a smaller proportion of the wave is transmitted into it, and a larger proportion is reflected back
- The more rigid/dense a medium is, the more the wave energy will be reflected back, less will be absorbed. This explains how sound can travel through walls
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Less dense boundary
- A pulse on the heavy rope will see that the light rope offers little resistance
- The light rope will be greatly affected by the heavy rope, so the transmitted pulse has a greater amplitude.
- The upright reflected pulse’s amplitude decreases, as some of the heavy rope’s energy has transmitted into the light rope
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Reflected Wave Fronts
- Two and three-dimensional waves, such as water waves, travel as wave fronts
- When close to the source, the wave fronts can show lots of curvature. Wave fronts can be curved or even be spherical when generated in three dimensions. When a wave has travelled long distances from its source, the wave front is plane (straight)
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Rays
- Direction of motion of any wave front is represented by a line drawn, perpindicular to the wave front, and in the direction the wave is moving
- Rays can illustrate the path of a wave front reflecting from a surface, showing the normal at which the wave hits the surface.
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Wave Effects
- Reflection: The boundary limit can cause a change in direction
- Refraction: The density of the medium can change the speed of a wave
- Diffraction: The bending of the direction of travel of a wave front as it passes through an aperture or by an obstacle; Significant diffraction occurs when the size of the aperture is about the same as the wavelength
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Law of Reflection
- The reflection of light waves obey the same laws of reflecton that apply to water waves
- The angle of incidence equals the angle of reflection: θi = θr.
- The normal is the line perpindcular to the surface
Regular v Diffuse Reflection
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- If parallel rays are incident on a smooth surface, they remain parallel on reflection. Common examples relate to light from plane mirrors, glossy painted surfaces, or still waters. Therefore, if irregularities in the surface are small compared to the wavelength of the incident light, regular reflection occurs
- Diffuse reflection is when parallel rays are reflected from rough/uneven surfaces. Rays are scattered in all directions. Parallel rays are reflected unevenly. While each ray obeys the law of reflection, the irregular surface causes the normal to be drawn in different direcions. Therefore, if the irregularities on the surface are comparable in size to the wavelength of the light, then more diffuse reflection occurs.
- Most surfaces display intermediate behaviour
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Superposition Principle
States that when two or more waves travel in a medium, the resulting wave, at any point is the sum of the displacements associated with the individual waves as a result of the superposition principle
Constructive Interference
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- When two transverse mechanical waves travel towards each other in a medium, the resulting wave is the vector sum of the two individual placements. The amplitude increases and the shape of the string resembles a combination of the two pulses. After interacting, the two pulses continue unchanged as a result of the superposition principle. When the two waves are added together, constructive superposition, or constructive interference has occured.
- Occurs when two waves that have particle displacements in the same direction meet, and add to a maximum
Destructive Interference
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- When a pulse with a positive displacement, meets one with a negative displacement, they vectorially add to a minimum; the two pulses momentarily cancel out; if the amplitude of one wave is larger the resulting wave will have a smaller amplitude, partial cancellation occurs. The sum of the pulse produces a wave of smaller magnitude known as destructive superposition. However, the pulses emerge from the interaction unchanged.
Superposition Principle in water
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- In some locations, constructive interference occurs and waves of large amplitude are seen
- Destructive interference occurs in other regions. Troughs arrive from the other source always cancel out the crests that arrives at these locations, the surface of the water remains relatively undisturbed
- Nodes are the areas where total destructive interference occurs = zero amplitude
- Antinodes are areas where total constructive interference occurs = maximum amplitude
- Diffraction and interference effects are only observed when energy is being carried by waves, not when energy is being carried by particles
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Interference between continuous waves when of the same frequency or wavelength
- When two waves of the same frequency or wavelength, are exactly in phase and are travelling in the same direction, therefore constructive interference will occur along the entire length of the wave
- The two waves do not need to have the same amplitude
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Interference: Different frequency or amplitude
- When two waves of different wavelengths are travelling in the same direction, and interfere, they combine
How are beats produced
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- Beat is produced by two sound waves: f1 and f2, of equal amplitude but different frequency. At X, the waves are in phase, and produce a larger amplitude (constructive interference). At Y, they are out of phase by 180degrees, resulting in smaller amplitude (destructive interference). At Z they are in phase again; when the two waves are in phase at X and Z, the resulting pressure variation, and volume is large. At Y, the waves are out of phase and the resulting amplitude and volume are zero)
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