Homework #4 Reminder - UW-Madison Department of...

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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

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

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.

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

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

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

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

Kind of waves• a traveling disturbance that transports

energy– Transverse - wiggling the rope at one end

– Longitudinal - scrunching a slinky

Transverse Waves

• In a transverse wave, each elementthat is disturbed movesperpendicularly to the wave motion

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

What are water waves?

• Water waves occur on the surface. They area kind of transverse wave.

On Earth On the sun

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

Longitudinal Wave Representedon a graph

• A longitudinal wave can also berepresented as a sine curve

• Compressions correspond to crests andstretches correspond to troughs

Description of a Wave

• Amplitude is themaximumdisplacement ofstring above theequilibrium position

• Wavelength, λ, isthe distancebetween twosuccessive pointsthat behaveidentically

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

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

Equation form

• Velocity = Wavelength / Period

• v = λ / T, or v = λf

• f = frequency = 1/T

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.

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

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”

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

mwhere

Fv =µ

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

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

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

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

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

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

Hearing

• Listening to the radio

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.

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

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

Ilog10=β

• Threshold of hearing is 0 dB• Threshold of pain is 120 dB• Jet airplanes are about 150 dB

Homework #4 Reminder - UW-Madison Department of...

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