Waves

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Waves

• This PowerPoint Presentation is intended for use
  during lessons to match the content of Waves and
  Our Universe - Nelson
• Either for initial teaching
• Or for summary and revision

Free powerpoints at http//www.worldofteaching.com
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Oscillations

• Going round in circles
• Circular Motion Calculations
• Circular Motion under gravity
• Periodic Motion
• SHM
• Oscillations and Circular Motion
• Experimental study of SHM
• Energy of an oscillator
• Mechanical Resonance

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Waves

• Travelling waves
• Transverse and Longitudinal waves
• Wave speed, wavelength and frequency
• Bending Rays
• Superposition
• Two-source superposition
• Superposition of light
• Stationary waves

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Going round in circles

• Speed may be constant
• But direction is continually changing
• Therefore velocity is continually changing
• Hence acceleration takes place

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Centripetal Acceleration

• Change in velocity is towards the centre
• Therefore the acceleration is towards the centre
• This is called centripetal acceleration

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Centripetal Force

• Acceleration is caused by Force (Fma)
• Force must be in the same direction as
  acceleration
• Centripetal Force acts towards the centre of the
  circle
• CPforce is provided by some external force eg
  friction

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Examples of Centripetal Force

• Friction
• Tension in string
• Gravitational pull

Friction
velocity
Tension
velocity
Weight
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Centripetal Force 2
What provides the cpforce in each case ?
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Centripetal force 3
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Circular Motion Calculations

• Centripetal acceleration
• Centripetal force

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Period and Frequency

• The Period (T) of a body travelling in a circle
  at constant speed is time taken to complete one
  revolution - measured in seconds
• Frequency (f) is the number of revolutions per
  second measured in Hz

T 1 / f f 1 / T
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Angles in circular motion

• Radians are units of angle
• An angle in radians arc length /
  radius
• 1 radian is just over 57º
• There are 2p 6.28 radians in a whole circle

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Angular speed

• Angular speed ? is the angle turned through per
  second
• ? ?/t 2p / T
• 2p whole circle angle
• T time to complete one revolution

T 2p/? 1/f
f ?/2p
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Force and Acceleration

• v 2p r / T and T 2p / ?
• v r ?
• a v² / r centripetal acceleration
• a (r ?)² / r r ?² is the alternative
  equation for centripetal acceleration
• F m r ?² is centripetal force

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Circular Motion under gravity

• Loop the loop is possible if the track provides
  part of the cpforce at the top of the loop ( ST )
• The rest of the cpforce is provided by the weight
  of the rider

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Weightlessness

• True lack of weight can only occur at huge
  distances from any other mass
• Apparent weightlessness occurs during freefall
  where all parts of you body are accelerating at
  the same rate

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Weightlessness
These astronauts are in freefall
Red Arrows pilots experience up to 9g (90m/s²)
This rollercoaster produces accelerations up to
4g (40m/s²)
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The conical pendulum

• The vertical component of the tension (Tcos?)
  supports the weight (mg)
• The horizontal component of tension (Tsin?)
  provides the centripetal force

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Periodic Motion

• Regular vibrations or oscillations repeat the
  same movement on either side of the equilibrium
  position f times per second (f is the frequency)
• Displacement is the distance from the equilibrium
  position
• Amplitude is the maximum displacement
• Period (T) is the time for one cycle or or 1
  complete oscillation

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Producing time traces

• 2 ways of producing a voltage analogue of the
  motion of an oscillating system

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Time traces
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Simple Harmonic Motion1

• Period is independent of amplitude
• Same time for a large swing and a small swing
• For a pendulum this only works for angles of
  deflection up to about 20º

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SHM2

• Gradient of displacement v. time graph gives a
  velocity v. time graph
• Max veloc at x 0
• Zero veloc at x max

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SHM3

• Acceleration v. time graph is produced from the
  gradient of a velocity v. time graph
• Max a at V zero
• Zero a at v max

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SHM4

• Displacement and acceleration are out of phase
• a is proportional to - x

Hence the minus
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SHM5

• a -?²x equation defines SHM
• T 2p/?
• F -kx eg a trolley tethered between two
  springs

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Circular Motion and SHM
T 2p/?

• The peg following a circular path casts a shadow
  which follows SHM
• This gives a mathematical connection between the
  period T and the angular velocity of the rotating
  peg