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Lecture on Waves

Lecture on Waves. 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. Waves. Travelling waves

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Lecture on Waves

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  1. Lecture on Waves www.assignmentpoint.com

  2. 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 www.assignmentpoint.com

  3. Waves • Travelling waves • Transverse and Longitudinal waves • Wave speed, wavelength and frequency • Bending Rays • Superposition • Two-source superposition • Superposition of light • Stationary waves www.assignmentpoint.com

  4. Goinground in circles • Speed may be constant • But direction is continually changing • Therefore velocity is continually changing • Hence acceleration takes place www.assignmentpoint.com

  5. Centripetal Acceleration • Change in velocity is towards the centre • Therefore the acceleration is towards the centre • This is called centripetal acceleration www.assignmentpoint.com

  6. Centripetal Force • Acceleration is caused by Force (F=ma) • 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 www.assignmentpoint.com

  7. Examples of Centripetal Force • Friction • Tension in string • Gravitational pull Friction velocity Tension velocity Weight www.assignmentpoint.com

  8. Centripetal Force 2 What provides the cpforce in each case ? www.assignmentpoint.com

  9. Centripetal force 3 www.assignmentpoint.com

  10. Circular Motion Calculations • Centripetal acceleration • Centripetal force www.assignmentpoint.com

  11. 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 / ff = 1 / T www.assignmentpoint.com

  12. Angles in circular motion • Radians are units of angle • An angle in radians = arc length / radius • 1 radian is just over 57º • There are2π = 6.28 radians in a whole circle www.assignmentpoint.com

  13. Angular speed • Angular speed ω is the angle turned through per second • ω = θ/t = 2π / T • 2π = whole circle angle • T = time to complete one revolution T = 2π/ω = 1/f f = ω/2π www.assignmentpoint.com

  14. Force and Acceleration • v = 2π r / T and T = 2π / ω • v = r ω • a = v² / r = centripetal acceleration • a = (r ω)² / r = r ω² is the alternative equation for centripetal acceleration • F = m r ω² is centripetal force www.assignmentpoint.com

  15. Circular Motion under gravity • Loop the loop is possible if the track provides part of the cpforceat the top of the loop ( ST ) • The rest of the cpforce is provided by the weight of the rider www.assignmentpoint.com

  16. 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 www.assignmentpoint.com

  17. Weightlessness These astronauts are in freefall Red Arrows pilots experience up to 9g (90m/s²) This rollercoaster produces accelerations up to 4g (40m/s²) www.assignmentpoint.com

  18. The conical pendulum • The vertical component of the tension (Tcosθ) supports the weight (mg) • The horizontal component of tension (Tsinθ) provides the centripetal force www.assignmentpoint.com

  19. 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 www.assignmentpoint.com

  20. Producing time traces • 2 ways of producing a voltage analogue of the motion of an oscillating system www.assignmentpoint.com

  21. Time traces www.assignmentpoint.com

  22. 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 www.assignmentpoint.com

  23. SHM2 • Gradient of displacement v. time graph gives a velocity v. time graph • Max veloc at x = 0 • Zero veloc at x = max www.assignmentpoint.com

  24. 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 www.assignmentpoint.com

  25. SHM4 • Displacement and acceleration are out of phase • a is proportional to - x Hence the minus www.assignmentpoint.com

  26. SHM5 • a = -ω²x equation defines SHM • T = 2π/ω • F = -kx eg a trolley tethered between two springs www.assignmentpoint.com

  27. Circular Motion and SHM T = 2π/ω • 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 www.assignmentpoint.com

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