Physics Beyond 2000

Physics Beyond 2000 Chapter 9 Wave Phenomena

Glossary • Wave: It is a periodic disturbance in a medium or in space. • There must be source(s) in periodic oscillation. • There is a transfer of energy from the source.

Glossary • Progressive waves (or travelling waves) The wave pattern is moving forwards. • Stationary waves (or standing waves) The wave pattern remains at the same position. Progressive and stationary transverse waves: http://www.geocities.com/yklo00/2Waves.html Stationary longitudinal wave: http://www.fed.cuhk.edu.hk/sci_lab/Simulations/phe/stlwaves.htm

Glossary • Mechanical waves: with medium for the vibration. • Electromagnetic waves: no medium is required. It is the electric field and magnetic field in vibration.

Glossary • Transverse wave: the direction of vibration is parallel to the direction of travel of the wave. • Longitudinal wave: the direction of vibration is perpendicular to the direction of travel of the wave. http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/waveType/waveType.html http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html http://webphysics.davidson.edu/Applets/TaiwanUniv/waveType/waveType.html

Glossary • Sinusodial wave: • Square wave: • Saw-toothed wave: Observe these wave patterns on a CRO.

Progressive Waves • The disturbance is propagating from a source to places. • Energy is transferred from the source to places. • Matter of medium is not transferred. It is vibrating. http://members.nbci.com/surendranath/Applets.html

water ripples Ripple is an example of progressive wave that carries energy across the water surfaces. http://www.colorado.edu/physics/2000/waves_particles/waves.html http://www.freehandsource.com/_test/ripple.html

water ripples Ripple is an example of progressive wave that carries energy across the water surfaces. wavefront ray source

Mechanical waves • In need of a material medium for the propagation of wave. • Examples are wave in a string, sound wave, water wave etc.

Electromagnetic waves • They can travel through a vacuum. • Speed of electromagnetic wave in vacuum is 3 × 108 ms-1. • Electromagnetic spectrum: http://www.colorado.edu/physics/2000/waves_particles/

Electromagnetic waves • Electromagnetic waves are transverse waves. • Electric field and magnetic field are changing periodically at right angle to each other and to the direction of propagation. http://www.fed.cuhk.edu.hk/sci_lab/Simulations/phe/emwave.htm Oscillation of charges: http://www.colorado.edu/physics/2000/waves_particles/wavpart4.html

Analytical Description of Progressive Waves • Speed of propagation (c) • Frequency (f) • Wavelength (λ) • Amplitude (a) • Period (T)

Analytical Description of Progressive Waves • T = • c = f. λ = where s the distance travelled in time t.

Example 1 • c = f. λ

Graphical Representation andPhase Relation • Each particle in the wave is performing a simple harmonic motion, oscillating about its equilibrium position. http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/wave/wave.html http://members.nbci.com/surendranath/Applets.html

Graphical Representation andPhase Relation • There is a phase difference between any two particles. • In phase (or phase difference = 0)

Graphical Representation andPhase Relation • There is a phase difference between any two particles. • In antiphase (or phase difference = π)

y x 0 Notation in the textbook • y = displacement of a vibrating particle. • x = distance of the particle from the source. y-x graph for a transverse wave (points along the path at a particular instant): c = speed of propagation  a

Notation in the textbook y-x graph for a transverse wave: C: crest T: trough direction of propagation C T

y > 0 y < 0 Notation in the textbook • y = displacement of a vibrating particle. • In transverse wave, y is positive if the particle is above the equilibrium position; y is negative if the particle is below the equilibrium position. Equilibrium position

Notation in the textbook y-x graph for a longitudinal wave: C:compression R:rarefaction C R

Equilibrium position Equilibrium position wave direction y < 0 y > 0 Notation in the textbook • y = displacement of a vibrating particle. • In longitudinal wave, y is positive if the particle displaces along the direction of the travel of the wave; y is negative if the particle displaces in the opposite direction of the travel of the wave.

Wave Speed and Speed of Particle • Wave speed c = • Speed of a particle vy = The wave is moving forward with a constant speed c. The particle is vibrating in a SHM with a changing speed.

Example 2 • Find the maximum speed of a vibrating particle. • The particle is in SHM with y = a.sin(t + o)

Phase Relationship • For the motion of a vibrating particle in SHM, y = a. sin(t + o) with o the initial phase. • In a wave, different particles have the different initial phase.

y direction of propagation 0 x x Phase difference between two points in a y-x graph P Q For two points with separation x in a wave with wavelength , their phase difference is in radian

y direction of propagation 0 x x Phase difference between two points in a y-x graph P Q Which point leads the other?

Phase difference between two points in a y-x graph y P direction of propagation 0 x R Compare points P and R. Which point leads the other?

Phase difference between two points in a y-x graph y P direction of propagation 0 x R Draw the new wave pattern after a time t. The whole wave pattern moves to the right.

Phase difference between two points in a y-x graph y P direction of propagation 0 x R Point P will move back to the equilibrium position from the crest after . Point R will move to the position of the crest from the equilibrium position.

Phase difference between two points in a y-x graph y P direction of propagation 0 x R After , P moves to the equilibrium position and R moves up to the position of the crest. So P leads R by

Phase difference between two waves in a y-x graph y y1 direction of propagation y2 0 x Two waves y1 and y2 of the same frequency are moving to the right simultaneously. What is the phase difference between these two waves?

The phase difference is Phase difference between two waves in a y-x graph y y1 direction of propagation y2 0 x x Measure the separation x of their crests ( choose x < /2 ).

Phase difference between two waves in a y-x graph y y1 direction of propagation y2 P 0 x Choose a point P in front of the waves. Which wave has its crest reach the point first? The first wave leads the second wave by .

Density variation along a longitudinal wave • The centres of compression have the highest density and highest pressure (for gas). C

Density variation along a longitudinal wave • The centres of rarefaction have the lowest density and lowest pressure (for gas). R

Density variation along a longitudinal wave • The crest of the density/pressure leads that of displacement by /2. x x

The phase difference is Example 3 • Ripple in water is transverse wave. • Hint:

Example 4 • Which one leads? • Keep the phase difference < .

y a 0 t T -a Displacement-time graph • Describe a particle of the wave at different time.

y a 0 t T -a Displacement-time graph • For a particle performing simple harmonic motion, y = a.sin(t + o) • It is a sinusoidal wave.

y a 0 t T -a Displacement-time graph • Other particles along the path are performing SHM at the same frequency but with a different phase o

y a P Q 0 t T -a Displacement-time graph • Two points P and Q are in the path of a wave.

Physics Beyond 2000