Waves: Intro Periodoic motion

Periodic Motion We are surrounded by oscillations – motions that repeat themselves Understanding periodic motion is essential for the study of waves, sound, alternating electric currents, light, etc. How many of you play an instrument? An object in periodic motion experiences restoring forces that bring it back toward an equilibrium position Those same forces cause the object to “overshoot” the equilibrium position Think of a block oscillating on a spring or a pendulum swinging back and forth past its equilibrium position Demonstrate

How does a wave vary in position and velocity with time How does a wave vary in position and velocity with time? - Full body Demonstrate - PVA graphs

Wave Motion The wave is another basic model used to describe the physical world (the particle is another example) Any wave is characterized as some sort of “disturbance” that travels away from its source Periodic waves are result of oscillations For example, sound waves produced by vibrating string On the same order as size of source

Definitions of a Waves A wave is a traveling disturbance that carries energy through space and matter without transferring mass. Transverse Wave: A wave in which the disturbance occurs perpendicular to the direction of travel (Light). Longitudinal Wave: A wave in which the disturbance occurs parallel to the line of travel of the wave (Sound). Surface Wave: A wave that has charact-eristics of both transverse and longitudinal waves (Ocean Waves). Wave types

Types of Waves Mechanical Waves: Require a material medium* such as air, water, steel of a spring or the fabric of a rope. Electromagnetic Waves: Light and radio waves that can travel in the absence of a medium. * Medium = the material through which the wave travels. The wave does not carry the medium with it. All waves carry momentum and energy.

Types of Waves In solids, both transverse and longitudinal waves can exist Transverse waves result from shear disturbance Longitudinal waves result from compressional disturbance Only longitudinal waves propagate in fluids (they can be compressed but do not sustain shear stresses) Transverse waves can travel along surface of liquid, though (due to gravity or surface tension) Sound waves are longitudinal Each small volume of air vibrates back and forth along direction of travel of the wave Earthquakes generate both longitudinal (4–8 km/s P waves) and transverse (2–5 km/s S waves) seismic waves (Quicktime) Also surface waves which have both components

Questions Which kind of wave is sound? (2) Which kind of wave are the ripples on a pond? (2) Which kind of wave is light? (2) Which kind of wave can exist in a vacuum? (2) Which kind of waves carry momentum and energy? Possible Answers: transverse, longitudinal, mechanical, electromagnetic, surface

Transverse Wave Characteristics Crest: The high point of a wave. Trough: The low point of a wave. Amplitude: Maximum displacement from its position of equilibrium (undisturbed position) Greater amplitude  Greater energy John Wiley & Sons

Transverse Wave Characteristics (cont.) Frequency(f): The number of oscillations the wave makes in one second (Hertz = 1/seconds). Wavelength(): The minimum distance at which the wave repeats the same pattern (= 1 cycle). Measured in meters. Velocity (v): speed of the wave (m/s). v = f Period (T): Time it takes for the wave to complete one cycle (seconds). T = 1/f

The Inverse Relationships v = f The Inverse Relationships The speed of a wave is determined by the medium in which it travels. Since velocity is constant for a given medium, the frequency and wavelength must be inversely proportional. As one increases, the other decreases Position Wavelength Frequency

The Inverse Relationships T = 1/f Similar to the inverse relationship for frequency and wavelength, a similar relationship exists for frequency and the period. Position Period Frequency

Review: Key characteristics of waves Amplitude: The height of the wave from node to antinode (transverse waves), or the distance between compression and rarefaction in a in a compressive wave. Measured in units describing the wave Wavelength: The distance traversed by a full cycle of the wave Node: The “zero point” of the wave Antinode: The extreme point of the wave (max or min amplitude) Period: The time between successive waves Frequency: The rate of occurrence of the wave (in Hertz or cycles / second) Antinode Node Amplitude Wavelength

Let’s bring these two waves to life Transverse wave: The direction of the oscillation of the atoms is perpendicular (or transverse) to the direction of the propagation of the wave Longitudinal or Compression wave: The direction of the oscillation of the atoms is along the same direction as the propagation of the wave

Wave Phase: In Phase and out of Phase

Speed of Waves Dependent on Medium Temperature Pressure Frequency (wavelength) What about light? Medium Wavelength (frequency) (temperature) (pressure)

Speed of Waves The relationship between wave speed, wavelength, and frequency is simple For a given temperature, pressure, material, etc. v = fl, where v is the speed, f is the frequency, and lambda is the wavelength. What is v for sound? What is v for light? What is v for a Slinky?

Speed of Waves Medium Speed (m/sec) Frequency Wavelength Sound 340 261 Light 300,000,000 700E-9 Ocean Wave 25 1 Tsunami 260 Earthquake P 2 Earthquake Surface 0.5 Guitar String 425 1m http://www.pbs.org/wgbh/nova/earth/japan-killer-quake.html

Key Ideas Waves transfer energy without transferring matter. Longitudinal waves like that of sound require a medium. Transverse waves such as electro-magnetic radiation do not require a medium. In transverse waves, displacement is perpendicular to the direction of the wave while in longitudinal waves, the displacement is in the same direction.