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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 /


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