waves 2 opt
TRANSCRIPT
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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
100s of free ppts fromwww.pptpoint.com library
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Oscillations1. Going round in circles
2. Circular Motion Calculations
3. Circular Motion under gravity
4. Periodic Motion
5. SHM
6. Oscillations and Circular Motion
7. Experimental study of SHM8. Energy of an oscillator
9. Mechanical Resonance
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Waves
10. Travelling waves
11. Transverse andLongitudinal waves
12. Wave speed, wavelengthand frequency
13. Bending Rays
14. Superposition
15. Two-source superposition
16. Superposition of light
17. Stationary waves
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Going round in circles
Speed may be constant But direction is continually
changing Therefore velocity iscontinually changing
Hence acceleration takesplace
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Centripetal Acceleration Change in velocity is
towards the centre
Therefore theacceleration istowards the centre
This is calledcentripetalacceleration
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Centripetal ForceAcceleration is caused byForce (F=ma)
Force must be in the samedirection as acceleration
Centripetal Force actstowards the centre of thecircleCPforce is provided bysome external force eg friction
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Examples of Centripetal Force Friction Tension in
string
Gravitationalpull
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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
Centripetalacceleration
Centripetalforce
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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 57 There are 2 = 6.28
radians in a whole circle
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Angular speed Angular speed is the
angle turned throughper second
= /t = 2 / T 2 = whole circle angle T = time to complete
one revolutionT = 2 / = 1/f
f = /2
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Force and Acceleration v = 2 r / T and T = 2 / v = r
a = v / r = centripetal accelerationa = (r ) / r = r is the alternativeequation for centripetal acceleration
F = m r is centripetal force
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Circular Motion under gravity
Loop the loop ispossible if the trackprovides part of thecpforce at the top
of the loop ( S T ) The rest of thecpforce is providedby the weight of
the rider
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Weightlessness
True lack of weight canonly occur at hugedistances from any other mass
Apparent weightlessnessoccurs during freefall where all parts of you bodyare accelerating at thesame rate
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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 samemovement on either side of the equilibrium position f times per second ( f is the frequency )
Displacement is the distance from the equilibriumposition
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 Motion 1
Period is independent of amplitude
Same time for a large swing anda small swingFor a pendulum this only works for angles of deflection up to about 20
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SHM 2
Gradient of displacement v. timegraph gives avelocity v. time graph
Max veloc at x = 0 Zero veloc at x = max
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SHM 3 Acceleration v. timegraph is produced
from the gradient of a velocity v. timegraph
Max a at V = zero Zero a at v = max
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SHM 4
Displacement andacceleration are out
of phase a is proportional to - x
Hence theminus
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SHM 5 a = - x equation defines SHM T = 2 / F = -kx eg a trolley tethered between two springs
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Circular Motion and SHM
The peg following a circular path casts ashadow which follows SHM
This gives a mathematical connectionbetween the period T and the angular velocity
of the rotating peg
T = 2 /