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Wave Motion --- motion of patternsWhen we talk about wave motion , we are talking, not about the motion of particles or extended objects as single object, but we are talking about the motion of pattern in an extended object, or in groups of objects.

The above figure shows a traveling wave in a rope.

If we consider motion of the individual pieces of the rope they are moving up and down in the frame of the picture.

The wave, however, is moving to the right.

There are 2 connections between these waves and SHM.

First the wave themselves are often shaped like sine curves.

Second, the motion of the pieces of the rope is SHM.

Continuous or periodic wave

http://kingfish.coastal.edu/physics/physlets/Waves/traveling_wave.html?textBox=5.0*sin%282.0*x-7.0*t%29

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Mathematical characterization of the wave.

The wavelength of the wave is the distance between any 2 repeating points in the pattern.

The Period

The period, T , is the time it takes for one wavelength to pass a certain point. So you picture yourself watching the wave at some point, and you start you stopwatch at some point, and when the same point in the wave pattern passes you, you stop the watch. The time you have measured is the period.

Speed of the wave.

During the time equal to the period the wave has traveled a distance of one wavelength. So to calculate the velocity of the wave we can say that

v=d t

=T

If we want to write the wave speed in terms of the frequency we have

f = 1T

so v= f

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Transverse and Longitudinal Waves

In the first kind of waves we pictured the material moves perpendicular to the direction of the motion of the wave pattern. This is called a transverse wave.

http://www.ngsir.netfirms.com/englishhtm/TwaveA.htm

In the (a.) picture above, that material is moving along the same line as the direction of the wave. Half of the time the material is moving in the same direction as the wave and the other half it is moving opposite to the direction of the wave.

http://www.youtube.com/watch?v=f66syH8B9D8&feature=player_embedded

Interference and superposition

There is a defining difference between particles whose motion we have been studying till now and the motion of waves.

No 2 particles can occupy the same space. Particles collide and create collisions

Waves, alternatively, can occupy the same space, and when they do what occurs is not collisions but superposition.

Since waves are patterns I can add 2 or more patterns together, and this is called superposition.

http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html

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If 2 patterns have the same direction in the motion of the medium then they will create a pattern whose displacement is larger than the 2 individual patters. This is called constructive interference.

If the patterns have motion in opposite directions, (a.) then the overlap of the patterns will cancel, called destructive interference.

If we have waves in 2 or 3 dimensions, the interference can create its own pattern.

http://www.falstad.com/wavebox/

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Standing Waves and Resonance

It is the interference of waves which under the right circumstances can create standing waves, which are waves in which the pattern does not move, but oscillates in the same space

http://thespoon7.tripod.com/wave.htm

It is standing wave which lead to resonance, in which small driving forces can lead to large amplitude oscillations.

Nodes and antinodes

A node is a point in the pattern where the is no motion.

An anti-node is a point in the pattern in which the motion is a maximum.

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Standing wave quantization

Standing wave only occur in systems of finite size.

In such such systems only certain length patterns are possible as standing waves.

These quantized standing waves form the basis of all musical instruments.

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The mass of the beam is 27 kg.

1. Calculate the tension in the cable.

a. 200 N b. 203 N c 206 N d. 209 N e. none

2. Calculate the magnitude of the force of the wall on the beam in the x direction.

a. 156N b 158 N c. 160N d. 162N e. none

c. Calculate the direction of the force of the wall on the beam.

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Ch 8 Prob 34

A grinding wheel is a uniform cylinder with a radius of 8.50 cm. and a mass of 0.580 kg.

The moment of inertia of a solid cylinder is 12

M R2

Calculate the applied torque needed to accelerate it from rest to 1500 rpm in 5 s if it is known to slow down from 1500 rmp to rest in 55.0 seconds.

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