Vibrations and Waves

Periodic Motion u Motion that follows the same path over equal time intervals u Include orbiting planets, moons, vibrating objects, pendulums

Simple Harmonic Motion u Periodic motion that vibrates about an equilibrium position (oscillation) u Force always tries to return object to equilibrium position u Amount of restoring force is directly proportional to the displacement from the equilibrium position

Simple Harmonic Motion u Distance of travel from center position is called amplitude u Time for one complete cycle is the period u Rate of motion is called frequency u Unit of frequency is the hertz (Hz) u Examples: Pendulum, mass bouncing on spring

The Pendulum u Simple pendulum is made up of cord and bob, which contains the mass u Swing of pendulum is simple harmonic motion -- repeated over equal time intervals through equilibrium position u Period depends only on length of pendulum and pull of gravity -- not on mass or distance of swing u Long pendulum has longer period than short pendulum

Waves u Vibration that travels forward through space is a wave u Examples: water waves, sound, light, x- rays, earthquakes u Waves transport energy, not matter u Material that carries the wave is called the medium: air is the medium for the disturbance of sound wave

Wave Types u Transverse Waves: motion of medium is perpendicular to direction of wave travel –water waves, vibrating strings, light –series of crests and troughs u Longitudinal Waves: motion of medium is parallel to direction of wave travel –sound waves, “Slinky” waves, earthquakes –series of high and low pressure areas

Wave Properties u Amplitude: height of wave from equilibrium position u Frequency (f): number of waves passing a point per second -- measured in hertz (Hz) –1 hertz = 1 vibration / second  Wavelength ( ): The distance between identical points on successive waves; measured in meters

Wave Properties u Period (T): the time for one complete wave cycle u Frequency and period are reciprocals; f = 1/T and T = 1/f

Wave Speed  Wave speed = frequency x wavelength; v=f u Wave speed depends on medium wave travels through u For waves of same type and speed, like light or sound, frequency and wavelength are inversely proportional

Reflection u Occurs at a boundary between two media u Part or all of wave is returned to original medium u Incident wave strikes boundary, reflected wave is returned u Wave may be inverted at reflection

The Law of Reflection u Angle of incidence = angle of reflection

Refraction u A change in direction of wave travel at a boundary between two media u Caused by change in wave speed u If wave slows down in new medium, it bends towards the normal; speeds up, wave bends away from normal u Wavelength changes, frequency does not

Refraction

Superposition Principle u When two or more waves intersect, each wave continues independently as if no other wave were present u Where waves overlap, the effect on the medium is the sum of the effects from the individual waves

Interference u The result of superposition of two or more waves of same type in the same space u If waves line up crest to crest, they are said to be in phase; constructive interference occurs and bigger wave results u If waves line up crest to trough, they are out of phase; destructive interference occurs and smaller wave results

Interference u Often waves are only partially in or out of phase with each other u If two waves are totally out of phase, complete cancellation can result u A series of waves can produce an interference pattern

Standing Waves u When two waves of equal amplitude and wavelength move through the same medium in opposite directions, a standing wave is produced u Parts of medium remain stationary and are called nodes u Other areas with maximum amplitude are antinodes

Standing Waves u Result of interference, both constructive and destructive u Usually created by wave reflecting back on itself u String and wind musical instruments use standing waves to produce sound

Diffraction u The bending of a wave behind a barrier or past a small opening u If wave passes through two small openings, an interference pattern is set up

Diffraction

Bow and Shock Waves u When wave source moves a same speed as wave travel, wave barrier appears ahead of moving source u If boat moves faster than wave speed, bow wave produced, spreading out behind u Supersonic aircraft produce 3-dimensional shock wave, heard as sonic boom

Bow and Shock Waves u Sonic boom not due to sound produced by aircraft but by disturbance of air by its passage u Bullets, whips also create sonic booms