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Transcript of Waves This PowerPoint Presentation is intended for use during lessons to match the content of Waves...
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
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 SHM
8. Energy of an oscillator
9. Mechanical Resonance
Waves10. Travelling waves
11. Transverse and Longitudinal waves
12. Wave speed, wavelength and frequency
13. Bending Rays
14. Superposition
15. Two-source superposition
16. Superposition of light
17. Stationary waves
Going round in circles
• Speed may be constant• But direction is continually
changing• Therefore velocity is
continually changing• Hence acceleration takes
place
Centripetal Acceleration
• Change in velocity is towards the centre
• Therefore the acceleration is towards the centre
• This is called centripetal acceleration
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
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
Angles in circular motion
• Radians are units of angle• An angle in radians
= arc length / radius• 1 radian is just over 57º• There are 2π = 6.28
radians in a whole circle
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
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
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
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
Weightlessness
This rollercoaster produces accelerations up to 4g (40m/s²)
These astronauts are in freefall
Red Arrows pilots experience up to 9g (90m/s²)
The conical pendulum
• The vertical component of the tension (Tcosθ) supports the weight (mg)
• The horizontal component of tension (Tsinθ) provides the centripetal force
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
Producing time traces• 2 ways of producing a voltage analogue
of the motion of an oscillating system
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
SHM2
• Gradient of displacement v. time graph gives a velocity v. time graph
• Max veloc at x = 0
• Zero veloc at x = max
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