Ch14 Waves

Wave Types Mechanical Waves: require a material medium to propagate. WaterRope SpringsSound 3 types of Mechanical Waves –Transverse –Longitudinal –Surface

Longitudinal Waves: The medium moves parallel to the direction of the wave.

Longitudinal Waves A Longitudinal: A wave in which the vibration is in the same direction that in which the wave is traveling. Notice how the atom in the box below never leaves the box even though the wave is obviously traveling to the right. Animation courtesy of Dr. Dan Russell, Kettering University

Transverse wave: the medium vibrates perpendicularly to the direction of travel.

Transverse Mechanical Waves A transverse wave is one in which the individual atoms or particles vibrate in a direction perpendicular to the direction of motion of the wave. Notice how the atoms in the box below never leave the box even though the wave is obviously traveling to the right. Animation courtesy of Dr. Dan Russell, Kettering University

Rotations t As the Wheel Turns Watch how the sine function (which demonstrates a wave) traces out as a wheel turns. The vertical axis represents horizontal position and the horizontal axis represents time. Rotations t

Simple Harmonic Motion Simple Harmonic Motion: Motion caused by a linear restoring force that has a period independent of amplitude. Period: The time required to repeat one complete cycle Amplitude: Maximum displacement from equilibrium.

Transverse wave: the medium vibrates perpendicularly to the direction of travel. The wave travels horizontally. Any one point on the wave travels vertically Transverse Wave e.g. Pianos Guitar String

Standing Waves Longitudinal Waves: The medium moves parallel to the direction of the wave. The wave travels horizontally. Any one point on the wave also travels horizontally.

Surface Wave Surface Waves: Are a mixture of both parallel and perpendicular motion.

HW Read CH14 Worksheet vibrations and Waves 1-8

Wave Pulse Wave Pulse: A single disturbance that travels through a medium A pulse can move in either direction

Hand Drawn Examples Transverse Longitudinal Pulse

Period (T): The shortest time interval during which motion repeats. Measures of a Wave Time (s)

Frequency (f): The number of complete vibrations per second. Measures of a Wave Time (s) Number of vibration (cycles)

Measures of a Wave Wavelength : The shortest distance where the pattern of the wave repeats Meters (m)

Measures of a Wave Crest: The highest point on a wave Trough: The lowest point on a wave

Measures of a Wave Amplitude: The maximum displacement from rest or equilibrium

Wave Examples Can two waves can have the same wavelength and velocity, but different amplitudes? The greater the amplitude the greater the energy.

Waves When these oscillations between two extremes are graphed wrt time, we see the following profile emerge. The Wavelength ( ) is the distance from the “same” point on two consecutive oscillations. The Amplitude (A) is the maximum displacement from zero. The Period (T) is the time between the same position on consecutive “humps.” The Frequency (f) describes how often an oscillation occurs. The high points on the wave are known as “crests.” The low points on the wave are known as “troughs.” 0 +A -A

Wave Velocity The velocity of a wave is the distance traveled divide by the time it takes to move

Example A sound wave from a starters pistol is heard 100m down the track at the finish line. a)How long did it take the starter to start the stop watch if he waited for the sound. b)How long if he started the stopwatch when he saw the smoke? c)How much faster do the runners times appear?

Example WS14.2 #1 A sound wave produced by a clock chime 515m away is heard 1.5s later. a) What is the speed of sound in air? b) The sound wave has a frequency of 436Hz. What is its period? c) What is its wavelength?

Practice Problems WS 14.2 –#’s 2,3 WS 14.3 –#’s 1,2

Wave Boundaries What happens when a wave hits a boundary between two mediums? –Part of the wave is transmitted –Part is reflected The amount that gets transmitted versus reflected depends on the difference between two mediums.

Wave Boundaries When a wave is transmitted from less dense to more dense, the reflected wave is inverted.

Wave Boundaries Reflection follow Newton’s 3 nd Law –The string pulls up on the wall –The wall pulls down on the string –The wall doesn't move –The string is reflected inverted.

Wave Boundaries example A pulse is sent along a spring. The spring is attached to a light thread which is attached to a wall. a)What happens when the pulse reaches the string? b)Is the pulse reflected erect or inverted? c)What happens when the transmitted pulse reaches the wall? d)Is this pulse erect or inverted?

Waves at Boundaries Reflected pulse Transmitted pulse Low Density MediumHigh Density Medium Note: Both amplitudes get smaller

Wave Boundaries example A pulse is sent along a light thread. The thread is attached to a spring which is attached to a wall. a)What happens when the pulse reaches the spring? b)Is the pulse reflected erect or inverted? c)What happens when the transmitted pulse reaches the wall? d)Is this pulse erect or inverted?

Waves at Boundaries High Density MediumLow Density Medium Reflected pulse Transmitted pulse

Wave Boundaries The frequency of a wave being transmitted from one medium to another does NOT change. e.g. If I’m moving a string up and down, I don’t change the velocity that I vibrate it.

Wave Demo’s Spring to a fixed boundary (more dense) Spring to a light string (less dense) Light string to spring Heavy spring to slinky.

Practice Problems Page 296 –#’s 5-8

Superposition of Waves Principle of superposition: Interference: Constructive Interference: Destructive Interference: Record these vocabulary terms and define their meaning using your text.

Superposition of Waves Principle of superposition: The displacement of a medium caused by two or more waves is the algebraic sum of each wave. Waves pass each other so the original wave continues unaltered. Interference is the result of the superposition of two or more waves.

Wave Superposition Constructive Interference 2 or more waves adding together to make a larger wave Antinode is the point of maximum displacement (i.e., where amplitude is largest)

Wave Superposition Destructive Interference Constructive Interference NodesAntinodes The blue wave below represents the sum of the 2 other waves.

Wave Superposition Graph A Wave Sum Constructive Interference Destructive Interference Antinodes Antinodes Nodes

Interference of Sine Waves When two or more waves occur in close proximity to one another, they produce interference patterns. Constructive Interference Destructive Interference 0 +A -A

Superposition of Waves Constructive Interference: Occurs when the displacements are in the same direction Destructive Interference: Occurs when the displacements are on opposite sides of equilibrium. Show excel demo

Practice Problems Sketch the resultant waveform when the center of the two waves are at the red boundary

Superposition of waves Node

Practice Problems WS 14.1 –# 9 –WS

End Ch 14 Chapter Quiz Moved standing waves to ch15

Standing Waves Standing Wave: Node: Antinode: Record these vocabulary terms and define their meaning using your text.

Standing Waves Standing Wave: has stationary nodes and antinodes. It is the results of identical waves traveling in opposite direction. Node: The medium is not displaced as the waves pass through Antinode: The displacement caused by interfering waves is largest.

Standing Waves In order for a standing wave to exist, there must be an identical wave traveling in the opposite direction Standing wave demo

Standing Waves Harmonics: Standing wave that consist of more than one pulse

Standing waves Fundamental Frequency: The lowest frequency that creates a standing wave in a given medium. Harmonics (overtones): frequencies with integer multiples of the fundamental frequency. These frequencies make up the harmonic series.

Harmonic Series in a string Length L

Reflection of Waves Normal Angle of incidence Angle of reflection Law of reflection

Diffraction Waves Node Antinode demo

Conservation of Energy Intro WS #2 PE PE + KE KE PE + KE PE

Reflected Transmitted

superposition A A B B