Vibrations and Waves Vibration—“a wiggle in time” Wave—“a wiggle in space and time” Back and forth vibratory motion = oscillatory motion. The oscillatory motion of a pendulum is an instance of simple harmonic motion. Period—the time of a back and forth swing. (Time/vibrations) Depends only on the length of the pendulum and the acceleration of gravity. A pendulum makes 20 vibrations in 40 seconds. Calculate its period. Period for the pendulum 40 seconds / 20 vibrations = 2 seconds

Wave Description A pendulum swinging over a moving piece of paper will trace out a sine curve. Wavelength—the distance between successive identical parts of the wave (crest to crest, for instance). Frequency—how frequently a vibration occurs. A complete back and forth vibration is one cycle. Hertz (Hz)—the unit of frequency. One cycle per second = 1 Hz Two cycles per second = 2 Hz “home”

Wave Motion The source of all waves is something that vibrates The frequency of the vibrating source and the frequency of the wave it produces is the same. If the frequency is known, then the period can be determined (and vice versa). Frequency = 1/period Period = 1/frequency Waves transfer energy, not matter between two points. The energy is carried by a disturbance in the medium, not by matter moving from one point to the other.

Wave Speed The speed of a wave depends on the medium through which it is moving. Sound travels through air at ~ 330 m/s Sound travels 4 times faster in water. Wave speed = frequency x wavelength v = fl If they are produced at the same time, high frequency sounds (small wavelength) reach your ears at the same time as low frequency sounds (large wavelengths).

Transverse and Longitudinal Waves Transverse wave—the motion of the medium is at right angles to the direction in which the wave travels. Longitudinal wave—the motion of the medium is along the same direction in which the medium travels.

Reflection – fixed end Reflection involves a change in direction of waves when they bounce off a barrier Boundary behavior—the behavior of a wave upon reaching the end of a medium. Consider a rope fixed to a heavy object at one end. The speed of the reflected pulse is the same as the incident pulse. The wavelength of the reflected pulse is the same as the wavelength of the incident pulse. The amplitude of the reflected pulse is less than the amplitude of the incident pulse (some of the energy was transferred to the other object).

Reflection- free end Consider now a rope that is free at both ends. The wave is not inverted in free-end reflections.

Reflection to a different medium The transmitted pulse (in the more dense medium) is traveling slower than the reflected pulse (in the less dense medium) The transmitted pulse (in the more dense medium) has a smaller wavelength than the reflected pulse (in the less dense medium) The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse (less dense medium)

Reflection to a different medium 2 The transmitted pulse (in the less dense medium) is traveling faster than the reflected pulse (in the more dense medium) The transmitted pulse (in the less dense medium) has a larger wavelength than the reflected pulse (in the more dense medium) The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse

Summary of Boundary Behavior The wave speed is always greatest in the least dense medium, The wavelength is always greatest in the least dense medium, The frequency of a wave is not altered by crossing a boundary, The reflected pulse becomes inverted when a wave in a less dense medium is heading towards a boundary with a more dense medium, The amplitude of the incident pulse is always greater than the amplitude of the reflected pulse.

Ripple Tank and Reflection The diagram at the right depicts a series of straight waves approaching a long barrier extending at an angle across the tank of water. The direction that these wavefronts (straight-line crests) are traveling through the water is represented by the blue arrow A ripple tank? A ripple tank is a large glass-bottomed tank of water that is used to study the behavior of water waves. A light typically shines upon the water from above and illuminates a white sheet of paper placed directly below the tank. A portion of light is absorbed by the water as it passes through the tank. A crest of water will absorb more light than a trough. So the bright spots represent wave troughs and the dark spots represent wave crests. As the water waves move through the ripple tank, the dark and bright spots move as well. As the waves encounter obstacles in their path, their behavior can be observed by watching the movement of the dark and bright spots on the sheet of paper.

The Law of Reflection The diagram below shows the reflected wavefronts and the reflected ray. the waves will always reflect in such a way that the angle at which they approach the barrier equals the angle at which they reflect off the barrier.

Refraction Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Refraction, or the bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves.

Refraction Waves that pass from deep water into shallow water will refract (bend), slow down, and their wavelength will decrease. What happens to wavelength as wave speed decreases?

Refraction Continued Light waves also refract when moving into a different medium.

Diffraction Diffraction—a change in direction of waves as they pass through an opening or around a barrier in their path. The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength. When the wavelength of the waves are smaller than the obstacle, no noticeable diffraction occurs. Can really be “seen” with sound waves

Interference More than one vibration or wave can exist at the same time in the same space. Interference pattern—the pattern produced by overlapping waves. Constructive interference (reinforcement)—when the crest of one wave overlaps the crest of another. Destructive interference (cancellation)—when the crest of one wave overlaps the trough of another.

Interference Two overlapping water waves produce an interference pattern. Areas of constructive interference are produced by waves that are in phase with one another. Areas of destructive interference are produces by waves that are out of phase with one another. Heavy lines represent crests, light lines represent troughs. Which letters represent constructive interference? Which ones destructive interference?

Standing Waves Standing wave—a wave in which the nodes remain stationary. Standing waves are produced when two waves of equal amplitude and wavelength pass through each other in opposite directions. The nodes are stable regions of destructive interference. The positions on a standing wave with the largest amplitudes are antinodes.

The Doppler Effect Consider a bug jiggling in water. The frequency of the waves produced by a stationary bug will be the same at points A and B. The frequency of the waves produced by a bug moving toward B at a speed less than wave speed will be higher at point B than point A.

The Doppler Effect When a sound source moves toward you, the pitch of the sound is greater. When a light source moves toward you, the frequency of the light is increased (blue shift) Light from a source moving away from you is red-shifted.

Bow Waves When the speed of the source in a medium is as great as the speed of the wave it produces, the waves pile up and create a barrier wave. When the source travels faster than the waves it produces, it outruns the wave crests and creates a V-shaped bow wave. Boats and supersonic aircraft create bow waves.