Waves and Sound

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

• Introduction (p 339)• One common way energy is transferred form on

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

• Waves (p 341-342)• • Waves: 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 all waves

Amplitude - height of the wave (A)Crests - peak or max height of the wave (A)Trough - lowest point or min of the wave (-A)Wavelength (l) - distance from crest to crest or from trough to troughFrequency (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) Period (T) time for a particle on a medium to make one complete vibrational cycle. T = 1/f

• 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 or l/T• 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.

• Combination Waves: Combination of both a longitudinal and transverse waves. Water waves and earth quakes are example of combination 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)

Comparison Between Transverse and Longitudinal Waves

• 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• Frequency (f): Number of cycle per time• Wave speed (v): Speed of the disturbance or wave through

the medium. • v = λ f

Example 12-4 Working with Waves: Determining Wavelength

• 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 so

• λ = v/ f = (3.00 x 108 m/s)/(3.80 x 1014s-1)

• λ = 7.894 x 10-7m

• λ = 789 nm

Example 12-5 Analyzing Waves

• Figure 12-26a shows a wave graph and figure 12-26b shows a vibration graph for a wave. Find the wave’s

• (a) Amplitude• A = 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)• Simple Speed• v = 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/period• Group Velocity Cg = beat pattern that moves together is called a wave

group

• 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 • In physics, periodic motion is something that is

repeated in equal intervals of time.

• 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).

See figure figure below for an example of a spring’s oscillating

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 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

• 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.

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. In fluid dynamics, dispersion of water waves generally refers to frequency dispersion. Frequency dispersion means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, and forced by gravity and surface tension. As a result, water with a free surface is generally considered to be a dispersive medium.

• 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.

• Besides frequency dispersion, water waves also exhibit amplitude dispersion. This is a nonlinear effect, by which waves of larger amplitude have a different phase speed from small-amplitude waves.

• Deep and shallow water waves: Deep do not fell bottom, shallow waves do

• 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. So 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.

• 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)

• 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.

Source IntensityIntensity

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

• Pitch: The sensation of a frequencies is commonly referred to as the pitch of a sound. A high pitch sound corresponds to a high frequency sound wave and a low pitch sound corresponds to a low frequency sound wave. Amazingly, many people, especially those who have been musically trained, are capable of detecting a difference in frequency between two separate sounds which is as little as 2 Hz. When two sounds with a frequency difference of greater than 7 Hz are played simultaneously, most people are capable of detecting the presence of a complex wave pattern resulting from the interference and superposition of the two sound waves. Certain sound waves when played (and heard) simultaneously will produce a particularly pleasant sensation when heard, are are said to be consonant. Such sound waves form the basis of intervals in music. For example, any two sounds whose frequencies make a 2:1 ratio are said to be separated by an octave and result in a particularly pleasing sensation when heard. That is, two sound waves sound good when played together if one sound has twice the frequency of the other. Similarly two sounds with a frequency ratio of 5:4 are said to be separated by an interval of a third; such sound waves also sound good when played together. Examples of other sound wave intervals and their respective frequency ratios are listed in the table below.

Interval 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

• The ability of humans to perceive pitch is associated with the frequency of the sound wave which impinges upon the ear. Because sound waves traveling through air are longitudinal waves which produce high- and low-pressure disturbances of the particles of the air at a given frequency, the ear has an ability to detect such frequencies and associate them with the pitch of the sound. But pitch is not the only property of a sound wave detectable by the human ear.

• 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 attack-decay envelope of the sound.

• Some investigators report that it takes a duration of about 60 ms to recognize the timbre of a tone, and that any tone shorter than about 4 ms is perceived as an atonal click. It is suggested that it takes about a 4 dB change in mid or high harmonics to be perceived as a change in timbre, whereas about 10 dB of change in one of the lower harmonics is required.

• Fundamental Frequency: The fundamental frequency (is distinguished from the natural frequency, which is a property of a resonant structure) of a periodic signal 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. The significance of defining the pitch period as the smallest repeating unit can be appreciated by noting that two or more concatenated pitch periods form a repeating pattern in the signal. However, the concatenated signal unit obviously contains redundant information. The fundamental frequency is the lowest frequency component of a signal that excites (imparts energy) to a system.

• The fundamental frequency of a sound wave in a tube with a single CLOSED end can be found using the following equation:

• • L can be found using the following equation:• • λ (lambda) can be found using the following equation:• • The fundamental frequency of a sound wave in a tube with either both ends OPEN or

both ends CLOSED can be found using the following equation:• • L can be found using the following equation:-

• 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. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency. Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 25 Hz, 50 Hz, 75 Hz, 100 Hz, etc.

• 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). 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

• Doppler 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.

• 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, also called biosonar, is the biological sonar used by several animals such as dolphins, shrews, most bats, and most whales. The term was coined by Donald Griffin, who was the first to conclusively demonstrate its existence in bats. Two bird groups also employ this system for navigating through caves, the so called cave swiftlets.

• 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.

• 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, typically to penetrate a medium and measure the reflection signature or supply focused energy. The reflection signature can reveal details about the inner structure of the medium. The most well known application of this technique is its use in sonography to produce pictures of fetuses in the human womb. There are a vast number of other applications as well.

• * 1 Ability to hear ultrasound• * 2 Diagnostic sonography• * 3 Biomedical ultrasonic applications• * 4 Industrial ultrasound• * 5 Ultrasonic cleaning• * 6 Ultrasonic humidifier• * 7 Ultrasound Identification (USID)• * 8 Ultrasound and animals• o 8.1 Bats• o 8.2 Dogs• o 8.3 Dolphins and whales• o 8.4 Fish• o 8.5 Moths• o 8.6 Rodents/insects• * 9 Sonochemistry• * 10 Ultrasonic disintegration• * 11 Ultrasonic range finding