Vibrations, Waves, & Sound
Chapters 25 & 26
25.1 Vibration of a Pendulum
•The period of the pendulum dependsonly on the length of a pendulum andthe acceleration of gravity.
Period
•The time it takes for one complete cycle ofmotion.
•Represented by the symbol T
•Unit of seconds
Frequency
•The number of cycles completed in a unit oftime (usually seconds)
•Represented by the symbol f
•Unit of s-1 (also known as Hertz)
Period and Frequency
•Period and frequency are inversely related.
•f = 1/T and T = 1/f
A plucked string vibrates back and forth10times each second.
•What is the period?
1/10 s
What is the frequency?
10 cycles per second (10 Hz)
What is a wave?
•A wave is an means by which energy istransferred from one place to another viaperiodic disturbances
Waves transfer energy
•Note that, while energy is transferred from point A topoint B, the particles in the medium do not movefrom A to B.
–Individual particles of the medium merely vibrateback and forth in simple harmonic motion
•The rate of energy transfer is proportional tothe square of the amplitude
–When amplitude is doubled, the energy carriedincreases by a factor of 4.
25.2 Wave Description
•The source of all waves is something thatvibrates.
•The back-and-forth vibratory motion of aswinging pendulum is calledsimple harmonic motion.
25.2 Wave Description
•A sine curve is a pictorial representation of awave.
Wave Parts
•Amplitude - the maximum displacement fromequilibrium.
•The high points on a wave are called crests.
•The low points on a wave are called troughs.
•The wavelength of a wave is the distance from onepart of a wave to the next identical part.
25.3 Wave Motion
•When energy is transferred by a wave from avibrating source to a distant receiver, nomatter is transferred between the two points.
Mechanical Waves
•Waves that require a physical medium to travelthrough.
•Examples of physical media are water, air, string,slinky.
Electromagnetic waves
•Waves that do not require a physical medium.
•Comprised of oscillating electric and magnetic fields
•Examples include x-rays, visible light, radio waves,etc.
25.4 Wave Speed
•You can calculate the speed of a wave bymultiplying the wavelength by thefrequency.
Wave speed
•Wave speed is determined completely bythe characteristics of the medium
–For an unchanging medium, wave speed isconstant
think!
If a water wave vibrates up and down two times each second andthe distance between wave crests is 1.5 m, what is the frequency ofthe wave? What is its wavelength? What is its speed?
Answer:
The frequency of the wave is 2 Hz; its wavelength is 1.5 m; and itswave speed is 3 m/s.
25.4 Wave Speed
25.5 Transverse Waves
•Particles of the medium move perpendicular to thedirection of energy transfer
•You should be able to identify crests, troughs,wavelength (distance traveled during one full cycle),and amplitude
Crest
Trough
25.6 Longitudinal Waves
•Particles of the medium move parallel to thedirection of energy transfer
•Be able to Identify compressions, rarefactions,wavelengths
CompressionsRarefactions
25.7 Interference
•The combination of two or more waves in amedium at the same time.
–Matter cannot occupy the same space at the sametime, but energy can.
25.7 Interference
•The Superposition Principle describes whathappens when waves interfere…
–Waves (energy) pass through each othercompletely unaffected
–The medium will be displaced an amount equal tothe vector sum of what the waves would havedone individually
Constructive Interference
-pulses to sameside of equilibrium
-resulting mediumdisplacement isgreater than originalwaves
-pulses continueunaffected
Destructive Interference
•Pulses on oppositesides of equilibrium
•Resulting displacementis less than at leastone of the originals
•Pulses continueunaffected
Complete Destructive Interference
Interference patterns
•Out of phase –destructiveinterference
•In phase –constructiveinterference
25.8 Standing Waves
•A wave pattern that results when two waves of thesame frequency, wavelength, and amplitude travel inopposite directions and interfere.
25.8 Standing Waves
•Only certain frequencies produce standing wavepatterns.
25.8 Standing Waves
•Nodes are areas of complete destructive interferenceand have no displacement
•Antinodes are areas of constructive interference andhave maxiumum displacement
25.9 The Doppler Effect
•As a wave source approaches, an observerencounters waves with a higher frequency.As the wave source moves away, an observerencounters waves with a lower frequency.
25.9 The Doppler Effect
•The greater the speed of the source, thegreater will be the Doppler effect.
25.9 The Doppler Effect
•The Doppler effect also occurs for light.
•When a light source approaches, there is anincrease in its measured frequency (blue shift)
•When it recedes, there is a decrease in itsfrequency (red shift)
26.1 The Origin of Sound
•All sounds originate in thevibrations of material objects.
•Pitch is the human perception offrequency
26.1 The Origin of Sound
•The normal range of human hearing is 20 to20,000 hertz.
•Sound waves with frequencies below 20 hertzare called infrasonic.
•Sound waves with frequencies above20,000 hertz are called ultrasonic.
26.2 Sound in Air
•Consider sound waves in a tube.
•When the prong of a tuning fork next to the tubemoves toward the tube, a compression enters thetube.
•When the prong swings away, in the oppositedirection, a rarefaction follows the compression.
•As the source vibrates, a series of compressionsand rarefactions is produced.
26.3 Media That Transmit Sound
•The speed of sound differs in differentmaterials.
•In general, sound is transmitted faster inliquids than in gases, and still faster in solids.
•Sound cannot travel in a vacuum.
26.4 Speed of Sound
•The speed of sound depends on thecharacteristics of the medium. A material’stemperature, mass of particles, density, andelasticity are all factors.
- In room temperature air, sound travels about 340 m/s
- In water, sound travels about 1200 m/s
- In aluminum, sound travels about 5000 m/s
26.6 Natural Frequency
•When any object composed of an elasticmaterial is disturbed, it vibrates at its ownspecial set of frequencies, which togetherform its special sound.
26.7 Forced Vibration
•Sounding boards are an important part of allstringed musical instruments because theyare forced into vibration and produce thesound.
26.8 Resonance
•If the frequency of a forced vibrationmatches an object’s natural frequency,resonance dramatically increases theamplitude.
•Resonance occurs wheneversuccessive impulses are applied to avibrating object in rhythm with itsnatural frequency.
Reflection
•The bouncing of a wave when it encountersthe boundary between two different media
Fixed End Reflection
•At a fixed boundary, waves are inverted as they arereflected.
Free End Reflection
•At a free boundary, waves are reflected on the sameside of equilibrium
