Phys Sci Lesson 24-25 Phys Sci Lesson 24-25 Waves and SoundWaves and Sound

Next test: Week 15 Dec 19/21

Week 16 Dec 30 class at my home: 10 - 1 PM

Reading AssignmentsModule 14 pp 341- 353Module 14 pp 353 - 364Homework AssignmentModule 14 Study Guide Questions p 365 # 1 -10 Module 14 Study Guide Questions p 365- 366 # 11 - 19

Prep Questions 11:(1) What is a wave?(2)  What are the types of waves?(3) What are the parts of waves?

Prep Questions 12:(1) What is sound?(2)  What is the Doppler Effect?

Introduction (p339)Introduction (p339)• One common way energy is transferred from on

place to another is a wave. In this module we will examine waves.

• Waves (p 341-342) : Oscillations of extended bodies made up of many objects such as water waves.

• Disturbances: Another term use to describe the waves.

• Medium: Material which a wave travels through.

Parts of WavesParts of Waves

•Amplitude - height of the wave (A) = ½ height (1/2 ypeak - ytrough)•Crests - peak or max height of the wave (A)•Trough - lowest point or min of the wave (-A)

•Wavelength (l or λ) - distance from crest to crest or from trough to trough

Cycle Terms of WavesCycle Terms of Waves

•Frequency (f) is the measure of how many waves hit a given point in a certain amount of time (cycles per second or the hertz - hz)

• Sound examples• Light examples

•Period (T) time for a particle on a medium to make one complete vibrational cycle. T = 1/f

T

Wave Motion TermsWave Motion Terms• Wave speed (v) sometimes called wave velocity- it is the speed a

specific wave has as it passes a given point – Note it is not velocity because this quality is independent of a direction. – Wave velocity is associated with movement a group of waves that act

together such as an ocean wave called propagation. The group of waves look like one wave that move in one direction.

– v = fl (v = fλ) or v= l/T (v=λ/T)– http://upload.wikimedia.org/wikipedia/commons/c/c7/Wave_opposite-group-phase-velocity.gif

• Propagation - wave propagation is any of the ways in which waves travel through a medium - related to wave speed

• Oscillation - the up and down motion - related to frequency

• Transmission medium (plural transmission media) is a material substance (solid, liquid or gas) which can propagate energy waves.– For example, the transmission medium for sound received by the ears is

usually air, but solids and liquids may also act as transmission media for sound.

– ALL waves excerpt for one (electromagnetic waves) requires a medium - something to move through.

Wave Motion TermsWave Motion Terms• Wave speed (v) sometimes called wave

velocity- it is the speed a specific wave has as it passes a given point – Note it is not velocity because this quality is

independent of a direction. – Wave velocity is associated with movement a

group of waves that act together such as an ocean wave called propagation. The group of waves look like one wave that move in one direction.

– v = fl (v = fλ) or v= l/T (v=λ/T)– http://upload.wikimedia.org/wikipedia/commons/c/c7/Wave_opposite-group-phase-velocity.gif

Wave Motion TermsWave Motion Terms• Propagation - wave propagation is any of the

ways in which waves travel through a medium - related to wave speed

• Oscillation - the up and down motion - related to frequency

• Transmission medium (plural transmission media) is a material substance (solid, liquid or gas) which can propagate energy waves.– For example, the transmission medium for sound

received by the ears is usually air, but solids and liquids may also act as transmission media for sound.

– ALL waves excerpt for one (electromagnetic waves) requires a medium - something to move through.

Two General Type of Waves (p 343)

• Transverse - wave that propagates perpendicular to its direction of occultation.

• Longitudinal - waves that propagates parallel to its direction of oscillation.

– Compression - area of compression (higher pressure/greater density) - like crest

– Rarefaction - pulled apart lower pressure/lower density - like trough.

Transfer waves Long waves Waves - Gen

Examples of Longitudinal WavesExamples of Longitudinal Waves

Comparison Between Transverse and Comparison Between Transverse and Longitudinal WavesLongitudinal Waves

• Amplitude (A): – Transverse waves: Amplitude is the greatest displacement of a particle.

A = ½(ypeak – ytrough)– Longitudinal waves: Amplitude is half the distance maximum and minimum

pressure (density) differences greatest displacement of a particle:A = ½(xmax – xmin)

• Wavelength (λ): – Transverse waves: the distance from peak to peak or trough to tough.

λ = xpeak2 – xpeak1 or xtrough2 – xtrough1– Longitudinal waves: the distance from compression zone to compression zone or

refraction zone to refraction zone.λ = xcomp2 – xcomp1 or xrefrac2 – xrefrac1

• Cycle: One cycle is completed in one wavelength (Same

• Frequency (f): Number of cycle per time (Same)

• Wave speed (v): Speed of the disturbance or wave through the medium. v = λ f (Same)

Examples of Transverse WavesExamples of Transverse Waves• Light Waves

• Top of water waves

• Earthquake "S" waves

Examples of Longitudes WavesExamples of Longitudes Waves• Sound

Waves

• Earthquake "P" waves

Combination WavesCombination Waves• Combination of both a longitudinal and

transverse waves. Water waves and earth quakes are example of combination waves.

• Water waves are examples of combination waves:– More transverse near the top– More compression waves below the surface – http://www.kettering.edu/physics/drussell/Demos/waves/wavemotion.html

Example 12-4 Working with Waves: Determining Wavelength

• Water - Top– distance from trough to crest is 30 feet – λ = 2 (30 feet) = 60 feet

• Sound – frequency of a high voice ~1000 Hz – Vsound = (331.5 +0.6T)m/sec (T must be in C)

at T = 20 (note: bad science on this page: 72F≠ 20C)• Vsound = 331.5 +0.6(20T)m/sec = 343.5 m/s

– v = λ f or λ = v/ f = (343.5 m/s)/1000 = 0.3435m*3.28 ft/m = 1.126 ft• Light

– A photon of red light has a speed of 3.00 x 108 m/s with a frequency 3.80 x 1014 Hz (s-1). What is its wavelength?

– Solution: – v = λ f (v is constant makes this a special case)– λ = v/ f = (3.00 x 108 m/s)/(3.80 x 1014s-1)– λ = 7.894 x 10-7m– λ = 789 nm

20˚C to F

• F = C (9/5) + 32• F = 20 9/5 + 32 = 4 (9) + 32 = 36 + 32 = 68 ˚F

20˚C = 68 ˚F

Example 12-5 Analyzing WavesFigure 12-26a shows a wave graph and figure 12-26b (BJP) shows a

vibration graph for a wave. Find the wave’s (a) AmplitudeA = ½(ypeak – ytrough) = ½(+10 cm – (-10 cm) = 20cm(b) Wavelength

λ = xcomp2 – xcomp1 = 25 cm – 5 cm = 20 cm = 0.2 m(c) Frequency

f = v/ λ = cycles/Δt = 1/(t2 – t1) = 1/ (2.5 s – 0.5 s) = 1/2s = 0.5 s-1(d) Period

T = 1/ f = 1/( 0.5 s-1) = 2 s(e) Wave propagation - movement of waves (see

http://en.wikipedia.org/wiki/Dispersion_%28water_waves%29)(f) Simple Speedv = λ f = 20 cm (0.5 s-1) = 10 cm/s = 0.2 m (0.5 s-1) = 0.1 m/s

Phase velocity Cp = wavelengh/periodGroup Velocity Cg = beat pattern that moves together is called a wave group

12a

12b

End week 11

• Begin week 12 – More specifics on waves

Some Specific Types of Waves• Standing or solitary wave:

Single or stationary wave

• Periodic Waves : wave that repeat over and over– Periodic waves are very

useful. The can carry:– Carry information – example

color.– Energy - EM waves – In physics, periodic motion is

something that is repeated in equal intervals of time.

Examples of Periodic Motion• Examples: a rocking chair, a bouncing ball, a

vibrating tuning fork, a swing in motion, the Earth in its orbit around the Sun, and a water wave. – In each case, the interval of time for a repetition, or

cycle, of the motion is called a period, – While the number of periods per unit time is called the

frequency. – Thus, the period of the Earth’s orbit is one year, and its

frequency is one orbit per year.– A tuning fork might have a frequency of 1,000 cycles

per second and a period of 1 millisecond (1 thousandth of a second).

An example of a spring’s oscillating motion

• http://www.youtube.com/watch?v=sTsUx-6CflI.

Spring Motion • Terms: rest or equilibrium position - position before stretching• Pull to mass on end of spring to y = -A then release

– For an ideal spring (no friction) the mass will go up and down between y = -A and +A

– Damping: Effect of friction in a real spring that weakens the oscillation with time

• Restoring Force (Fr): Force that tends to return the spring to the equilibrium position - gravitational force pulls it down and force of spring pulls it up– Total amount of energy remains constant going back and forth from

PE to KE – Measuring spring constant: http://www.youtube.com/watch?v

=s1jRAF1C9VA&feature=related

Spring Motion• The motion is characterized by:

– its amplitude (which is always positive), its period, the time for a single oscillation,

– its frequency, the reciprocal of the period (i.e. the number of cycles per unit time),

– and its phase, which determines the starting point on the sine wave.

– The period and frequency are constants determined by the overall system,

• while the amplitude and phase are determined by the initial conditions (position and velocity) of that system.

• The resorting force (Fr) - the forces that bring the motion back towards the equilibrium position.

The Electromagnetic WavesLight (EM) Waves are very unusual in that the are transverse waves that require no medium. More in Mod 15

Water Waves• (See http://

paws.kettering.edu/~drussell/Demos/waves/wavemotion.html)

• Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. – As a wave travels through the waver, the particles travel in clockwise

circles. – The radius of the circles decreases as the depth into the water

increases. Surface gravity waves, moving under the forcing by gravity, propagate faster for increasing wavelength. For a certain wavelength, gravity waves in deeper water have a larger phase speed than in shallower water. In contrast with this, capillary waves only forced by surface tension, propagate faster for shorter wavelengths.

• There are three basic types of – Deep water waves: Deep do not feel bottom, – Intermediate water waves: Feel bottom a little bit– Shallow water waves: Strongly feel the bottom

Deep Water Wave

Shallow Water Wave

deep-water: http://www.classzone.com/books/earth_science/terc/content/visualizations/es1604/es1604page01.cfm?chapter_no=visualization

http://www.youtube.com/watch?v=7yPTa8qi5X8

Breakers: http://www.youtube.com/watch?v=8y1MkFZSwIs&feature=related

Shallow: http://www.youtube.com/watch?v=SQv7I2MdvZc

L < 2 depthL < 2 depth L between L between 1/20 and 2 1/20 and 2 depth depth L >1/20 depthL >1/20 depth 1H/7W 1H/7W

Sound Waves• Sound waves are longitudinal pressure waves

that propagate through a substance that comes from a vibrating body.– The more dense a substance the faster sound travels

through it.• sound travels fastest through solids, less quickly through

liquids and slowest through gasses.• Process of hearing:

– Something vibrates, – the vibrations cause compression and refraction of

the air around the vibrating object – causing a pressure wave that propagates to your ear, – that causes the eardrum to vibrate, – then tiny bones in the inner ear which causes a nerve

impulse that the brain can interpret as sound.

Sound Waves• Characteristics (Qualities) of Sound:• Intensity(I): The sound intensity, (acoustic intensity)

is defined as the sound power Pac transmitted per unit area A. The usual context is the noise measurement of sound intensity in the air at a listener's location. I = Pac/A = Pac/4r2.

• Loudness (β): Loudness as heard by a human is the quality of a sound that is a subjective measure related to sound intensity and sound pressure. Loudness is also affected by parameters other than sound pressure, including frequency and duration.

• β = (10 dB) log (Is/(10-12/W/m2)

Sound Waves• Decibels: The decibel (dB) is used to measure sound intensity *and other electronic,

signals and communication intensities). • The dB is a logarithmic unit used to describe a ratio. The scale for measuring

intensity is the decibel scale. • The threshold of hearing is assigned a sound level of 0 decibels (abbreviated 0 dB);

– this sound corresponds to an intensity of 1*10-12 W/m2. • A sound which is 10 times more intense ( 1*10-11 W/m2) is assigned a sound level of

10 dB.• A sound which is 10*10 or 100 times more intense ( 1*10-10 W/m2) is assigned a

sound level of 20 db. • A sound which is 10*10*10 or 1000 times more intense ( 1*10-9 W/m2) is assigned a

sound level of 30 db. • A sound which is 10*10*10*10 or 10000 times more intense ( 1*10-8 W/m2) is

assigned a sound level of 40 db. • Observe that this scale is based on powers or multiples of 10. If one sound is 10x

times more intense than another sound, then it has a sound level which is 10*x more decibels than the less intense sound. The table below lists some common sounds with an estimate of their intensity and decibel level.

Sound WavesSource Intensity Intensity

Level# of Times

Greater Than TOH

Threshold of Hearing (TOH) 1*10-12 W/m2 0 dB 100

Rustling Leaves 1*10-11 W/m2 10 dB 101

Whisper 1*10-10 W/m2 20 dB 102

Normal Conversation 1*10-6 W/m2 60 dB 106

Busy Street Traffic 1*10-5 W/m2 70 dB 107

Vacuum Cleaner 1*10-4 W/m2 80 dB 108

Large Orchestra 6.3*10-3 W/m2 98 dB 109.8

Walkman at Maximum Level 1*10-2 W/m2 100 dB 1010

Front Rows of Rock Concert 1*10-1 W/m2 110 dB 1011

Threshold of Pain 1*101 W/m2 130 dB 1013

Military Jet Takeoff 1*102 W/m2 140 dB 1014

Instant Perforation of Eardrum 1*104 W/m2 160 dB 1016

Sound Waves• Pitch: The sensation of a frequencies is commonly

referred to as the pitch of a sound. – High pitch sound corresponds to a high frequency sound wave – Low pitch sound corresponds to a low frequency sound wave.

• Quality: Sound "quality" or "timbre" describes those characteristics of sound which allow the ear to distinguish sounds which have the same pitch and loudness. – Timbre is then a general term for the distinguishable

characteristics of a tone. – Timbre is mainly determined by the harmonic content of a sound

and the dynamic characteristics of the sound such as vibrato and the envelope of the sound.

Sound WavesInterval Frequency Ratio Examples

Octave 2:1 512 Hz and 256 Hz

Third 5:4 320 Hz and 256 Hz

Fourth 4:3 342 Hz and 256 Hz

Fifth 3:2 384 Hz and 256 Hz

Sound Waves• Fundamental Frequency: The fundamental

frequency is the inverse of the pitch period length. The pitch period is, in turn, the smallest repeating unit of a signal. One pitch period thus describes the periodic signal completely.

• Natural Frequency: 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.

Sound Waves• Harmonics: In acoustics and telecommunication, a

harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. – For example, if the fundamental frequency is f, the harmonics

have frequencies f, 2f, 3f, 4f, etc. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 25 Hz, 50 Hz, 75 Hz, 100 Hz, etc.

• Resonance and resonant frequencies: Resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. – These are known as the system's resonant frequencies (or

resonance frequencies). – At these frequencies, even small periodic driving forces can

produce large amplitude oscillations, because the system stores vibrational energy.

Sound Waves• Speed of Sound: The speed of a sound wave in air depends upon the properties of

the air, namely the temperature and the pressure. The pressure of air (like any gas) will affect the mass density of the air (an inertial property) and the temperature will affect the strength of the particle interactions (an elastic property).

• The speed of sound is the distance travelled during a unit of time by a sound wave . In dry air at 20 °C (68 °F), the speed of sound is 343.2 metres per second (1,126 ft/s). This is 1,236 kilometres per hour (768 mph), or about one kilometer in three seconds or approximately one mile in five seconds.

• At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through air is approximated by the following equation:

• v = 331 m/s + (0.6 m/s/C)•T• where T is the temperature of the air in degrees Celsius. Using this equation to

determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.

• v = 331 m/s + (0.6 m/s/C)•T • v = 331 m/s + (0.6 m/s/C)•(20 C)• v = 331 m/s + 12 m/s• v = 343 m/s

• 1 meter / second = 2.24 mph

Doppler EffectDoppler Effect• The Doppler effect (or Doppler shift), named after Austrian physicist

Christian Doppler who proposed it in 1842, is the change in frequency and wavelength of a wave for an observer moving relative to the source of the waves.

– It is commonly heard when a vehicle sounding a siren approaches, passes and recedes from an observer.

– The received frequency is increased (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is decreased during the recession.

• For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted.

• The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately.

• For waves which do not require a medium, such as light or gravity in special relativity, only the relative difference in velocity between the observer and the source needs to be considered.

– Doppler Effect

– Doppler Explanation

Doppler EffectDoppler Effect• If the moving source is emitting waves through a medium with an actual frequency f0,

then an observer stationary relative to the medium detects waves with a frequency f given by

– f = (v/v+vs)fo • where v is the speed of the waves in the medium and vs is the speed of the source

with respect to the medium (positive if moving away from the observer, negative if moving towards the observer).

• A similar analysis for a moving observer and a stationary source yields the observed frequency (the receiver's velocity being represented as vr):

– f = [(v+vr/v)]fo • where the same convention applies: vr is positive if the observer is moving away from

the source, and negative if the observer is moving towards the source.

• These can be generalized into a single equation with both the source and receiver moving.

• which can be written as: f = [(v+vr)/(v+vs)]fo

– Where vs,r is the source to receiver velocity radial component.With a relatively slow moving source, vs,r is small in comparison to v and the equation approximates to f = [(1(v/vs-r)]fo

– vs-r = vs - vr

Doppler Example:

• A stationary source emits a sound wave of 5000 Hz. An object approaches the source with a velocity of 3.5 m/s. What is the frequency of the wave as experienced by the object?

• v of sound ≈ 343 m/s • f'object =[(v + vr/v) f0 ]· = 5000 Hz [(343 m/s + 3.5 m)/343 m/s)]·• = 5000 Hz (346.5/343) = 5000 Hz.(1.0102) = 5051 Hz• • f'object = [(1-(vs-r/v)]fo = [(1-(0-3.5m/s/343 m/s)]5000 Hz = [(1-(-

0.01020)]5000 Hz• = [(1+ 0.01020)]5000 Hz =(1.01020)5000 Hz = 5051 Hz

Some Uses of Sound• Hearing: ability to perceive sound by

detecting vibrations via an organ such as the ear.

• Sonar: (sound navigation and ranging) is a technique that uses sound propagation (usually underwater) to navigate, communicate with or detect other vessels.

Echolocation• Echolocation, also called biosonar, is the

biological sonar used by several animals such as dolphins, shrews, most bats,cave swiftlets (birds), and most whales.

• Echolocating animals emit calls out to the environment and listen to the echoes of those calls that return from various objects in the environment. They use these echoes to locate, range, and identify the objects. Echolocation is used for navigation and for foraging (or hunting) in various environments.

EcholocationEcholocation

• Echo Location

• Echo Location

Ability to Perceive Sound

Ultrasound - Putting sound to work • Ultrasound is cyclic sound pressure with a frequency greater

than the upper limit of human hearing. – Although this limit varies from person to person, it is approximately 20

kilohertz (20,000 hertz) in healthy, young adults and thus, 20 kHz serves as a useful lower limit in describing ultrasound.

– The production of ultrasound is used in many different fields:

• Medical Diagnostic Ultrasonic Applications• Ultrasonic Cleaning - cleans deleicate items• Ultrasonic Humidifier - cool mist - fog• Ultrasound Identification (USID)• Ultrasound and animals

– Bats, Dogs, Dolphins and whales, Fish, Moths, Rodents/insects• Ultrasonic disintegration• Ultrasonic range finding