Waves

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? - 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.

Mechanical waves For now, we will concentrate on mechanical waves traveling through a material medium –The wave is the propagation of the disturbance: they do 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? (3) Which kind of wave are the ripples on a pond? (3) 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?

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). 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

v = f 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 Wavelength Frequency The Inverse Relationships

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

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

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

Speed of Waves MediumSpeed (m/sec)FrequencyWavelength Sound Light300,000,000700E-9 Ocean Wave251 Tsunami260 Earthquake P2 Earthquake Surface 0.5 Guitar String4251m

Waves at Fixed Boundaries A wave incident upon a fixed boundary will have its energy reflected back in the opposite direction. Note that the wave pulse is inverted after reflecting off the boundary. Example of Waves at Fixed Boundaries Example of Waves at Fixed Boundaries

Interference Interference occurs whenever two waves occupy the same space at the same time. Law of Linear Superposition: When two or more waves are present at the same time at the same place, the resultant disturbance is equal to the sum of the disturbances from the individual waves.

Constructive Wave Interference Constructive Interference – Process by which two waves meet producing a net larger amplitude.

Destructive Wave Interference Destructive Interference – Process by which two waves meet canceling out each other.

Standing Waves Standing Wave: An interference pattern resulting from two or more waves moving in opposite directions with the same frequency and amplitude such that they develop a consistent repeating pattern of constructive and destructive interference. Node: The part of a standing wave where interference is destructive at all times (180 o out of phase). Antinode: The part of the wave where interference is maximized constructively. Standing Wave

Continuous Waves When a wave impacts a boundary, some of the energy is reflected, while some passes through. The wave that passes through is called a transmitted wave. A wave that is transmitted through a boundary will lose some of its energy. Electromagnetic radiation will both slow down and have a shorter wavelength when going into a denser media. Sound will increase in speed when transitioning into a denser media. Speed of Light in different mediums

Incident + Reflected Wave Higher speed Longer wavelength Lower speed Shorter wavelength Transmitted Wave Continuous Waves – Higher Speed to Lower Speed Note the differences in wavelength and amplitude between of the wave in the two different mediums Displacement Boundary v1v1 v2v2 -v 1 Note: This phenomena is seen with light traveling from air to water.

Waves at Boundaries Examples of Waves at Boundaries Wave Types (Cutnell & Johnson) Wave Types Waves - Colorado.edu Other Examples

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.

Key Ideas Waves travel at different speeds in different mediums. Light slows down when going from air to a liquid or solid. Sound speeds up when going from air to a liquid or solid. Waves can interfere with one another resulting in constructive or destructive interference.

Continuous Waves – Lower Speed to Higher Speed Note the differences in wavelength and amplitude between of the wave in the two different mediums Incident + Reflected Wave Lower speed Shorter wavelength Higher speed Longer wavelength Transmitted Wave -v 1 v2v2 v1v1 Displacement Boundary

Affects of sound waves Shatter glass! Transmit energy!

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Wave Videos Reflection off a sea wall: Big wave at beach: =player_embedded#at=131 Tacoma narrows bridge: SdPEn0AIxT7w8QF?p=tacoma+narrows+bridge&b=21&tnr=20 SdPEn0AIxT7w8QF?p=tacoma+narrows+bridge&b=21&tnr=20 &ved=0CJEBEBYwDQ&url=http%3A%2F%2Fwww.joe.ie%2Fnews%2Fcurrent- affairs%2Fvideo-these-huge-waves-forced-pedestrians-to-flee-the-footpath-in-tramore- this-morning%2F&ei=YrZVU5GrFJCnsATLxYDYDw&usg=AFQjCNEee0VBKDWk- FqbGCzim6T6AgEF0g&sig2=WGLREQeIb59HyB3EiTcpJA

Review of Springs Classic example of periodic motion: –Spring exerts restoring force on block: – k = spring constant (a measure of spring stiffness) –“Slinky” has k = 1 N/m ; auto suspensions have k = 10 5 N/m –Movie of vertical spring: Elastic potential energy stored in spring: – U el = 0 when x = 0 (spring relaxed) – U el is > 0 always – We do not have freedom to pick where x = 0 – U el conserves mechanical energy (Hooke’s Law)

Shock Absorbers Shock absorbers provide a damping of the oscillations –A piston moves through a viscous fluid like oil –The piston has holes in it, which creates a (reduced) viscous force on the piston, regardless of the direction it moves (up or down) –Viscous force reduces amplitude of oscillations smoothly after car hits bump in road –When oil leaks out of the shock absorber, the damping is insufficient to prevent oscillations Shock absorber is example of an underdamped oscillator (see also critically damped and overdamped)

Properties of Waves Superposition principle: The overlap of 2 or more waves (having small amplitude) results in a wave that is a point-by-point summation of each individual wave (constructive interference) (destructive interference)

Properties of Waves Traveling waves can both reflect and transmit across a boundary between 2 media –Reflected wave pulse is inverted (not inverted) if wave reaches a boundary that is fixed (free to move)