Vibrations and Waves

Good Vibrations!

At the heart of every wave Do the moving vibration walking demo Is a vibration. All waves begin with a vibration A vibration is a wiggle in space; something wiggles in time but does go anywhere. A wave is a wiggle that goes somewhere; it is a wiggle in both time and space

Wave Motion A wave is the motion of a disturbance Mechanical waves require Some source of disturbance (a vibration) A medium that can be disturbed All waves carry energy and momentum Not all waves are mechanical.

Types of Waves – Transverse In a transverse wave, each element that is disturbed moves in a direction perpendicular to the wave motion

Types of Waves – Longitudinal In a longitudinal wave, the elements of the medium undergo displacements parallel to the motion of the wave A longitudinal wave is also called a compression wave

Amplitude of a Vibration A = Δx Symbol: A Formula: A = ±Δx

Amplitude Amplitude, A, is the distance from the most extreme point to the equilibrium point. Amplitude is a length, so it is measured in meters

Period Period, T, is the time it takes to get through one complete cycle - for example, through all the positions shown here. The unit of period is a second

Frequency Frequency, f, is the number of complete cycles an object completes in a second. The unit for frequency is cycles/second, or “Hertz” (Hz)

Frequency and Period Frequency is the # of cycles per second Period is the # of seconds per cycles Notice: they are reciprocals of each other f = 1/T T = 1/f

Wave Speed Remember that the “normal” speed, or velocity, equation is . . . v = d/t And for waves, the speed still has the symbol v For distance, we’ll use the length of one wave, λ For time, we’ll use the period, T

Wavespeed, continued v = λf v = λ/T Old style Wave style Speed, v Wavespeed, v Distance, d Wavelength, λ Time, t Equation: v=d/t Period, T Equation: v = λ/T V=λ/T which is the same as v=λ(1/T) but (1/T) = f, therefore v = λf v = λ/T

Traveling Waves Try this! Use a snakey spring. Explore: the shape of the wave when it reflects Explore: the speed of the wave – what can make it change? Flip one end of a long rope that is under tension and fixed at one end The pulse travels to the right with a definite speed A disturbance of this type – where one-half a wave to a few waves travels along -- is called a traveling wave

Tsunami Feb 27, 2010 Website for Hilo footage – Feb 27, 2010 Thailand footage, 2006 (2.5 million deaths)

Standing Wave There are 3 nodes and 2 antinodes in the photo A standing wave has nodes (no amplitude) and antinodes (full amplitude)

Waveform – A Picture of a Wave The brown curve is a “snapshot” of the wave at some instant in time The blue curve is later in time The high points are crests of the wave The low points are troughs of the wave

Longitudinal Wave Represented as a Sine Curve A longitudinal wave can also be represented as a sine curve Compressions correspond to crests and stretches correspond to troughs Also called density waves or pressure waves

Description of a Wave A steady stream of pulses on a very long string produces a continuous wave The blade oscillates in simple harmonic motion Each small segment of the string, such as P, oscillates with simple harmonic motion

Amplitude and Wavelength Amplitude is the maximum displacement of string above the equilibrium position Wavelength, , is the distance between two successive points that behave identically

Speed of a Wave v = ƒ  Is derived from the basic speed equation of distance/time This is a general equation that can be applied to many types of waves

Interference of Waves Two traveling waves can meet and pass through each other without being destroyed or even altered Waves obey the Superposition Principle If two or more traveling waves are moving through a medium, the resulting wave is found by adding together the displacements of the individual waves point by point Actually only true for waves with small amplitudes

Constructive Interference Two waves, a and b, have the same frequency and amplitude Are in phase The combined wave, c, has the same frequency and a greater amplitude Show Physlet

Constructive Interference in a String Two pulses are traveling in opposite directions The net displacement when they overlap is the sum of the displacements of the pulses Note that the pulses are unchanged after the interference

Destructive Interference Two waves, a and b, have the same amplitude and frequency They are 180° out of phase When they combine, the waveforms cancel

Destructive Interference in a String Two pulses are traveling in opposite directions The net displacement when they overlap is decreased since the displacements of the pulses subtract Note that the pulses are unchanged after the interference

Wave Superimposition Animation zonalandeducation.com/.webloc

Reflection of Waves – Fixed End Whenever a traveling wave reaches a boundary, some or all of the wave is reflected When it is reflected from a fixed end, the wave is inverted The shape remains the same

Reflected Wave – Free End When a traveling wave reaches a boundary, all or part of it is reflected When reflected from a free end, the pulse is not inverted

Resonance - a special instance of constructive interference Almost everything has a natural frequency This is the frequency at which an object “wants” to vibrate If you cause an item to vibrate at its natural frequency, the vibrations will add together Demo: singing rod, standing wave in a string Application: microwave oven, swings

Reflection angle The angle of incidence is equal to the angle of reflection Pass out mirrors to verify this!

For Honors students: θi = θr Notice that the incident and reflected angles are measured from the normal

Refraction

Refraction Waves don’t always travel in straight lines. When they bend due to a change in speed, we call this refraction

Diffraction When a wave bends around a boundary, it’s called diffraction