Fri. Oct 1 Phy107 Lecture 11
Homework #4 Reminder
• Chap. 6– Concept: 36– Problems 14, 18
• Chap. 8– Concept: 8, 12, 30, 34– Problems 2, 10
• Due Wed. 10/6
Fri. Oct 1 Phy107 Lecture 11
Chapter 8: Wave Motion• A wave is a sort of motion
– But unlike motion of particles
• A propagating disturbance– The rope stays in one place– However something is moving
Fri. Oct 1 Phy107 Lecture 11
Wave properties
1) Speed is characteristic of the mediumelastic properties and inertia (mass) density
2) obey the principle of superposition - twosuperposed disturbances add or subtract
3) transfer energy along the direction ofpropagation.
Fri. Oct 1 Phy107 Lecture 11
But what moves?
• http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html• Mechanical waves require
– Some source of disturbance– A medium that can be disturbed– Some physical connection between or mechanism though
which adjacent portions of the medium influence eachother
• Waves transport energy
Fri. Oct 1 Phy107 Lecture 11
Waves can reflect
• Whenever a traveling wavereaches a boundary, someor all of the wave isreflected
• When it is reflected from afixed end, the wave isinverted
Fri. Oct 1 Phy107 Lecture 11
Waves can pass through each other
• Two pulses are traveling inopposite directions
• The net displacement whenthey overlap is the sum ofthe displacements of thepulses
• Note that the pulses areunchanged after the passingthrough each other
Fri. Oct 1 Phy107 Lecture 11
Continuous wave
• Can generate a wave that occupies all of therope by continuing to shake the end up anddown.
• Nee new terms to describe this continuouswave.
• Period, frequency, wavelength
Fri. Oct 1 Phy107 Lecture 11
Kind of waves• a traveling disturbance that transports
energy– Transverse - wiggling the rope at one end
– Longitudinal - scrunching a slinky
Fri. Oct 1 Phy107 Lecture 11
Transverse Waves
• In a transverse wave, each elementthat is disturbed movesperpendicularly to the wave motion
Fri. Oct 1 Phy107 Lecture 11
Longitudinal Waves
• In a longitudinal wave, the elements ofthe medium undergo displacementsparallel to the motion of the wave
• A longitudinal wave is also called acompression wave
Fri. Oct 1 Phy107 Lecture 11
What are water waves?
• Water waves occur on the surface. They area kind of transverse wave.
On Earth On the sun
Fri. Oct 1 Phy107 Lecture 11
Waveform – A Picture of a Wave
• Just like the pulse, acontinuous wave moves.
• The red curve is a“snapshot” of the waveat some instant in time
• The blue curve is later intime
• A is a crest of the wave• B is a trough of the wave
Fri. Oct 1 Phy107 Lecture 11
Longitudinal Wave Representedon a graph
• A longitudinal wave can also berepresented as a sine curve
• Compressions correspond to crests andstretches correspond to troughs
Fri. Oct 1 Phy107 Lecture 11
Description of a Wave
• Amplitude is themaximumdisplacement ofstring above theequilibrium position
• Wavelength, λ, isthe distancebetween twosuccessive pointsthat behaveidentically
Fri. Oct 1 Phy107 Lecture 11
Period and frequency of a wave
• Period: time required to complete one cycle– Unit = seconds
• Frequency = 1/Period = rate at which cyclesare completed– Units are cycles/sec = Hertz
Fri. Oct 1 Phy107 Lecture 11
Frequency, wavelength, andvelocity are related
• Period: Time required for source to emit onecycle
• Wavelength: spatial length of one cycle.• One wavelength must be gone before the
next one comes.• Must move one wavelength ( λ ) in one
Period ( T ).• Velocity = Wavelength/Period
Fri. Oct 1 Phy107 Lecture 11
Equation form
• Velocity = Wavelength / Period
• v = λ / T, or v = λf
• f = frequency = 1/T
Fri. Oct 1 Phy107 Lecture 11
Periodic waves
• Shake one end of a string up and down withperiod T (frequency f=1/T). The height (upor down) is the amplitude.
• Peaks move at speed v so are separated bydistance (wavelength) λ=vT = v/f.
• The wave can shake a fixed object with thatfrequency.
Fri. Oct 1 Phy107 Lecture 11
Examples
• The speed of sound in air is 340 m/s.• A source period of 1 Hz=1/s produces a
wavelength of λ=v/f= 340 m• A string vibrating at frequency f= 340 Hz
produces a wavelength λ=v/f = 1 m
Fri. Oct 1 Phy107 Lecture 11
Wave quantities summaryo Time of one COMPLETE up and down motion
– one period T = 1/f– one wavelength in one period
o Velocity of disturbance (wave or phase)velocity
o Particles don’t move with v (only up-and-down) or (back and forth)
v = λf• v depends only on properties of “medium”
Fri. Oct 1 Phy107 Lecture 11
Speed of a Wave on a String
• The speed on a wave stretched under sometension, F
• The speed depends only upon the propertiesof the medium through which thedisturbance travels
L
mwhere
Fv =µ
µ=
Fri. Oct 1 Phy107 Lecture 11
Producing a Sound Wave• Sound waves are longitudinal waves traveling through a medium• A tuning fork can be used as an example of producing a sound wave
• A tuning fork will produce apure musical note
• As the tines vibrate, theydisturb the air near them
• As the tine swings to theright, it forces the airmolecules near it closertogether
• This produces a high densityarea in the air– Area of compression
• Tine swings to left– Area of rarefaction
Fri. Oct 1 Phy107 Lecture 11
Sound from a Tuning Fork
• As the tuning fork continues to vibrate, asuccession of compressions and rarefactionsspread out from the fork
• A sinusoidal curve can be used to representthe longitudinal wave– Crests correspond to compressions and troughs to
rarefactions
Fri. Oct 1 Phy107 Lecture 11
Speed of Sound
• The speed of sound is higher in solids than in gases– The molecules in a solid interact more strongly, elastic property
larger
• The speed is slower in liquids than in solids– Liquids are softer, elastic property smaller
• Speed of waves on a string
propertyinertial
propertyelasticv =
€
v =Fµ
Tension
Mass per unit length
Fri. Oct 1 Phy107 Lecture 11
Examples
• The speed of sound in air is 340 m/s.• A source period of 1 Hz=1/s produces a
wavelength of L=v/f= 340 m• A string vibrating at frequency f= 340 Hz
produces a wavelength L=v/f = 1 m
Fri. Oct 1 Phy107 Lecture 11
Speed of Sound in a Solid Rod
• The speed depends on the rod’scompressibility and inertial properties
– Y is the Young’s Modulus of the material– The density of the material, ρ
ρ=
Yv
Fri. Oct 1 Phy107 Lecture 11
Speed of Sound in a Fluid
• In a liquid, the speed depends on thefluid’s compressibility and inertia
– B is the Bulk Modulus of the fluid– The density of the fluid: ρ
ρ=
Bv
Fri. Oct 1 Phy107 Lecture 11
Hearing
• Listening to the radio
Fri. Oct 1 Phy107 Lecture 11
Real sounds
• Most sounds are not purely sinusoidal• They have a frequency, and a wavelength,
but the structure can be quite complicated.• This structure (waveform) is part of what
makes different sounds sound different.• In addition, the way they turn on and off is
quite important in recognizing a sound.
Fri. Oct 1 Phy107 Lecture 11
Various Intensities of Sound
• Threshold of hearing– Faintest sound most humans can hear– About 1 x 10-12 W/m2
• Threshold of pain– Loudest sound most humans can tolerate– About 1 W/m2
• The ear is a very sensitive detector ofsound waves
Fri. Oct 1 Phy107 Lecture 11
The decibel scale• The sensation of loudness is logarithmic in the human hear
• The intensity level or the decibel level of the sound, β:
• Io is the threshold of hearing: I0 = 1.0 x 10-12 W/m2
oI
Ilog10=β
• Threshold of hearing is 0 dB• Threshold of pain is 120 dB• Jet airplanes are about 150 dB