waves2

waves2 - Transcript

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

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Oscillations
1 2 3 4 5 6 7 8 9 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
10 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

Examples of Centripetal Force
Friction Tension in string Gravitational pull

Centripetal Force 2

What provides the cpforce in each case

Centripetal force 3

Circular Motion Calculations
Centripetal acceleration Centripetal force

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 57 There are 2 6 28 radians in a whole circle

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

T 2 1 f f 2

Force and Acceleration
v 2 r T and T 2 v r a v r centripetal acceleration a r r r is the alternative equation for centripetal acceleration F m r 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

These astronauts are in freefall

Red Arrows pilots experience up to 9g 90m s
This rollercoaster produces accelerations up to 4g 40m s

The conical pendulum

The vertical component of the tension Tcos supports the weight mg The horizontal component of tension Tsin 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

Time traces

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 20

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

SHM4
Displacement and acceleration are out of phase a is proportional to x

Hence the minus

SHM5
a x equation defines SHM T 2 F kx eg a trolley tethered between two springs

Circular Motion and SHM T 2

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