11.3. Waves and Wave Propertiesdrlaurenceanderson.weebly.com/uploads/3/8/...waves.pdf · wave...
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11.3. Waves and Wave Properties
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Oscillations produce waves
Consider a group of swings at a playground. Each one is an oscillator. If we tie them one to another with ropes, and then start to swing in the first one, the connecting ropes will cause the other swings to start oscillating as well.
You have created a travelling disturbance.
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Waves
A wave is a disturbance that propagates from one location to another, carrying energy as it travels.
It is important to distinguish between the motion of the wave itself and the motion of the individual particles. A wave (PE and KE) can propagate long distances while the particles move only locally.
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Wave Creation
A wave pulse can be created on a string by a quick up-and-down motion. Because the molecules in the
string are attached by bonds, the upward moving molecules on one end will pull the adjacent molecules upward, which in turn will pull the molecules next to them upward, etc., and the wave disturbance will propagate. The particles do not.
Simple harmonic motion will produce a sine wave.
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Types of Waves
Transverse waves
The particles oscillate perpendicular to the direction of wave propagation
E.g. a wave that moves horizontally while the particles oscillate vertically around a fixed location.
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Types of Waves
Longitudinal waves
The particles oscillate parallel to the direction of wave propagation
E.g. a wave that moves along the x-axis while the particles oscillate along the x-axis around a fixed location.
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Sound waves are longitudinal waves
molecules in contact with it. These air pressure fluctuations (not the air molecules) propagate outward.
The ear drum detects sound in the same way.
A vibrating drum membrane causes alternate compressions and rarefactions of the density of air
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Combination waves
Only longitudinal waves can propagate through a fluid of constant density, because any transverse
motion in such a fluid would not experience a restoring force.
However, if and where there is a density gradient
within a fluid, and at the interface between fluids of different density, transverse waves may
propagate.
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Combination waves
Surface water waves are a
combination of transverse and
longitudinal waves.
So are waves
that travel through the
ground due to earthquakes.
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Wave Properties
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Wave Properties
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Wave Properties
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Wave Properties
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Example 1
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Types of Waves
Mechanical waves travel through matter---i.e. require matter for propagation. Sound waves and water waves are examples of mechanical waves.
Electromagnetic waves can travel through a vacuum. Radio waves and light waves are examples of electromagnetic waves. EM waves can travel through matter as well, e.g. glass.
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Waves travel at different speeds in different materials
The speed of a wave is determined by the properties of the material, or medium, through which it travels. A medium can be a solid, liquid or gas.
In general, waves travel faster in a medium that is hard, and slower in a medium that is squishy (compressible). For example, sound waves travel at 343 m/s in air, 1400 m/s in water, and 5960 m/s in steel.
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Speed of a longitudinal wave
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Material
Steel
Aluminum
Marble
Concrete
Bone
Brick
Wood
Mercury
Water
Ethyl alcohol
Air (at STP)
Elastic Modulus of compressibility
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Wave speeds also depend on various properties of the medium
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Speed of a wave on a cord
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Wave Reflection
An echo is an example of wave reflection. The sound wave “bounces” (reflects) off a solid object and travels back.
In general, waves reflect when they hit a barrier. The nature of the reflected wave depends on the type of barrier.
In the case of an echo, distance to the barrier also matters, since sound travels at 343 m/s.
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Wave Reflection: Inverted
When a string is anchored firmly to a wall, an incoming upward wave pulse will exert an upward force on the wall. The wall will exert an equal and opposite force on the string. Therefore, on reflection, the wave is inverted.
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Wave Reflection: Non-Inverted
When the far end of a string is free to move, an incoming wave pulse will move the ring upward and then back down---just like the motion that created the wave. Therefore, on reflection, the wave is not inverted. This is the case for a water wave.
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Wave Reflection: Observations
Fixed-end reflection: Free-end reflection:
Time 1:
Time 2:
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Partial Reflection: 1-D
If a light rope is tied to a heavy rope---i.e. there is a transition to a new medium---partial reflection will occur. The frequency of the transmitted wave will be
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Partial Reflection: 1-D
Partial reflection also occurs for light waves.
Incoming light Reflected light
Transmitted light
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Two-Dimensional Waves
For 2-D or 3-D waves, we can identify wave fronts, meaning all the points forming a wave crest. A line perpendicular to the front and in the direction of propagation is called a ray, (a). Wave fronts far from their source have such a large radius of curvature that they are approximately flat, and are called plane waves, (b).
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Two-Dimensional Reflection
For the reflection of a 2-D plane waves, the angle of the reflected rays and wave fronts will equal the angle of the incident (incoming) rays and wave fronts.
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Refraction
slower medium
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Refraction Moving into a slower medium, the rays become more perpendicular to the interface. That is, the angle of refraction is less than
the angle of incidence.
Similarly, the ray of a wave going from a slower medium to a faster one would bend away from the perpendicular.
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Refraction We can calculate the angle of refraction as follows:
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Laser Demo showing reflection and refraction
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Diffraction
When waves encounter an obstacle, there will be a “shadow region” behind the object.
However the waves will gradually bend around behind the object. This is called diffraction.
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Diffraction
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Diffraction
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Diffraction
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Waves Carry Energy
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Wave Energy