Vibrations and Waves Vibration—“a wiggle in time” Wave—“a wiggle in space and time”; a disturbance that travels through a medium from one location to another location 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.

What do trials 1-5 tell you? What about trials 6-8? The data convincingly show that wave frequency does not affect wave speed. An increase in wave frequency caused a decrease in wavelength while the wave speed remained constant. What do trials 1-5 tell you? What about trials 6-8?

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). Wavelength is lamda

Wave recap "a wave is a disturbance moving through a medium.“ Medium could be water, air, a rope, a slinky and are distinguished by their properties (material, density, temperature, elasticity, ect) These properties describe the material not the wave itself Waves are distinguished from each other based on amplitude, frequency, wavelength

Wave speed wave speed depends upon the medium through which the wave is moving. Only an alteration in the properties of the medium will cause a change in the speed.

CYU TRUE or FALSE: Doubling the frequency of a wave source doubles the speed of the waves. FALSE! The speed of a wave is unaffected by changes in the frequency.

Solve for wave speed

Solve for wave speed 3.5 m/s 2.5 m/s 2.1 m/s 2.2 m/s

CYU As the wavelength of a wave in a uniform medium increases, its speed will ____ Decrease Increase Remain the same As the wavelength of a wave in a uniform medium increases, its frequency will ____

CYU As the wavelength of a wave in a uniform medium increases, its speed will ____ Remain the same, the speed of a wave is not affected by the wavelength of the wave As the wavelength of a wave in a uniform medium increases, its frequency will ____ Decrease, wavelength and frequency are inversely proportional to each other

The water waves below are traveling along the surface of the ocean at a speed of 2.5 m/s and splashing periodically against Wilbert's perch. Each adjacent crest is 5 meters apart. The crests splash Wilbert's feet upon reaching his perch. How much time passes between each successive drenching? Answer and explain using complete sentences.

Answer to previous slide If the wave travels 2.5 meters in one second then it will travel 5.0 meters in 2.0 seconds. If Wilbert gets drenched every time the wave has traveled 5.0 meters, then he will get drenched every 2.0 seconds.

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.

Sound

The Origin of Sound All sounds are produced by the vibrations of material objects. Vibrating material sends a disturbance through a medium (usually air) in the form of a longitudinal wave. Under normal conditions, the frequency of the source = the frequency of the waves produced. Pitch—our subjective impression of the frequency of a sound. People with normal hearing can perceive pitches with frequencies from 20 Hz to 20,000 Hz. Infrasonic—sound waves with frequencies below 20 Hz. Ultrasonic—sound waves with frequencies above 20,000 Hz.

Sound in Air and Media that Transmit Sound Compression—a pulse of compressed air. Rarefaction—a region (pulse) of low pressure air. Remember: It is the pulse that travels; not the medium. In general, sound is transmitted faster in liquids than gases, and still faster in solids. Sound cannot travel in a vacuum.

The Sonic Spectrum – all mechanical, longitudinal waves.

Sound Ranges Infrasonic – less than 20 Hz Ultrasonic – more than 20,000 Hz Range of Human Hearing 20 – 20,000 Hz 0 – 120 dB

Driver Type Minimum Frequency Maximum Frequency Subwoofer < 20Hz 300-3kHz Mid Woofer 3kHz Midrange 300Hz Tweeter 1.5kHz > 20kHz Super Tweeter 10kHz 30kHz Typical Loudspeaker Driver Ranges

Approximate Range (Hz) Species Approximate Range (Hz)  human 64-23,000 dog 67-45,000  cat 45-64,000  cow 23-35,000  horse 55-33,500  sheep 100-30,000  rabbit 360-42,000  rat 200-76,000  mouse 1,000-91,000  opossum 500-64,000  guinea pig 54-50,000  hedgehog 250-45,000  raccoon 100-40,000 ferret 16-44,000  chinchilla 90-22,800  bat 2,000-110,000  beluga whale 1,000-123,000 elephant 16-12,000  porpoise 75-150,000 goldfish 20-3,000  catfish  50-4,000  tuna  50-1,100  bullfrog  100-3,000  tree frog canary  250-8,000  parakeet  200-8,500  cockatiel owl  200-12,000  chicken  125-2,000 

What do these sound like? We hear from 20-20000 Hz. Will 2000 Hz sound “high” or “low” pitched?

Speed of Sound Distance and time Wavelength and frequency Characteristics of the material the sound is traveling in

Speed of Sound In air, sound travels about 330 meters per second. Water vapor in the air increases this speed slightly. Increased temperature also increases this speed. Each degree increase above 0o C increases the speed of sound by 0.60 m/s. Sound travels 4 times faster in water than in air and 15 times faster in steel than in air. Sound travels faster through elastic materials than inelastic materials. Elasticity—the ability of a material to change shape in response to a force and then regain its initial shape. Example: Steel Example of an inelastic material: putty

Speed of Sound in Air Sound Travels Faster in Hotter Air

At 25°C

At -25°C

“tubes”

Decibels – a measure of the relative intensity of sounds.

Normal Conversation – 60 dB

85 decibels - prolonged exposure can cause gradual hearing loss 85 decibels - prolonged exposure can cause gradual hearing loss. 100 decibels - no more than 15 minutes prolonged exposure recommended 110 decibels - regular exposure of more than one minute risks permanent hearing loss without hearing protection.  

Loudest Sounds Ever! The Tunguska event 315 June 30, 1908 Space shuttle 165-170 blue whale 188 The Tunguska event 315 June 30, 1908 400,000 Watt speakers 135-145 decibel fireworks 145-150 dragster 155-160

Important Decibel Ideas This is a “relative” (comparing) scale. Humans can distinguish about 1 dB. 10dB higher “sounds” 2x louder. Logarithmic, not linear. 10x more energy = 10dB higher 100x more energy = 20dB higher 1000x more energy = 30dB higher 10,000,000x more energy = 70dB higher

Loudness The intensity of a sound is proportional to the square of the amplitude of a sound wave. Decibel (db)—the unit of intensity. Loudness—a physiological sensation that differs from person to person. Loudness varies nearly as the logarithm of intensity. 0 db = the lower threshold of hearing for a normal ear. 10 db is 10 x more intense than 0 db. 20 db is 10 x more intense than 10 db and 100 x more intense than 0 db.

Beats

Two similar sounds played together

Resonance

Natural Frequency of Vibration The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object.

Chalkboard – Tuning Fork Forced Vibration Chalkboard – Tuning Fork

Resonance

Tacoma Narrows Bridge http://youtu.be/3mclp9QmCGs

Resonance Examples Breaking Wine Glass http://www.youtube.com/watch?v=17tqXgvCN0E&feature=related