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In a material medium, the resorting force is provided by intermolecular forces. If a molecule is disturbed, the restoring forces exerted by its neighbors tend to return the molecule to its original position, and it begins to oscillate. In so doing, it affects adjacent molecules, which are in turn set into oscillation. This is propagation of wave.

Bonds can be represented by springs

The spring force is restoring force.

A pulse: a single disturbance that travels through a medium

medium – the substance or object in which the wave is travelling.

What is a wave? A disturbance that moves through something rather vague!

Why are waves important?

waves carry energy

sometimes a lot

and sometimes even more

the energy from the sun comes to us along electromagnetic waves– light waves

The important thing is that when a wave travels in a medium, parts of the medium do not end up at different places. The energy of the source of the wave is carriedto different parts of the medium by the wave.

Travelling/Continuous/Progressive wave:

• continuous distrurbance• transfer energy from one place to another. • without a net motion of the medium through which they travel. • they all involve oscillations – SHM, of one sort or another.

Depending on the direction of oscilations of the medium relative to the direction of propagation of the wave (energy flow), there are three basic categories and many more combinations:

Not everything that we call a wave is a wave actually: If it results with matter pining up it is not a wave in physics sense.

Transverse wave• The particles of the medium oscillate perpendicular to the

direction of energy transfer/propagation of the wave. • Earthquake secondary waves, waves on a stringed

musical instrument, waves on the rope, • EM waves: light, radio waves, microwaves…

Longitudinal/Compression wave

oscillations of air molecules are in the same direction as energy transfer

• The particles of the medium oscillate parallel to the direction of energy transfer/propagation of the wave.

• Sound waves in any medium, shock waves in an earthquake, compression wave along a spring…

direction of energy transfer

rarefaction – region in a medium with low pressure, low density. compression – region in a medium with high pressure, high density.

Relationship between pressure (longitudinal) and transverse graphs

• the diaphragm of the speaker moves in and out

• the air molecules jiggle back and forth in the same direction as the wave/ energy transfer

• the same as the change of density in the case of shock eartquake wave

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Transverse wave graph looks very similar to the actual wave. For a longitudinal wave the graph is not so easy to see.

They need medium to propagate, where paricles of the medium oscillate as the wave passes through.

There are two types of waves regarding medium.

1. Mechanical waves

• a disturbance that propagates through a medium – solids, liquids or gases thus transferring energy from one place to another.

• waves on strings

• waves in water – ocean waves• sound waves – pressure waves in gas,

solid or liquid• in short, every wave that is NOT EM wave• As the disturbance moves, the parts of the

material (segment of string, air molecules) execute harmonic motion (move up and down or back and forth)

Disturbance travels not the medium

• a disturbance that propagates through a medium – solids, liquids or gases thus transferring energy from one place to another.

• waves on strings• waves in water

– ocean waves• sound waves – pressure waves in air, solid

or liquid• in short, every wave that is NOT EM wave• As the disturbance moves, the parts of the

material (segment of string, air molecules) execute harmonic motion (move up and down or back and forth)

The other ones, ELECTROMAGNETIC WAVES, do not need medium to propagate. They come to us from faraway stars traveling through a vacuum. Of course, they can travel through a medium, but when they travel through medium, they do definitely not make particles of the medium vibrate at EM frequency. Just imagine window oscillating at frequency of visible light, ~ 1015 Hz. On the other hand when a sound wave (mechanical wave) travels through a window it will make glass vibrate at that frequency.

2. Electromagnetic waves

Electromagnetic Waves

A wave of energy. The electric and magnetic field oscillate (change magnitude and direction)

1. EM emission occurs when electron fall from an excited state to a state of lower energy. Energy of EM wave equals the electron’s change in energy.

+

before photon emission ~ 10-8 s later – photon emission

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+

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EM waves are produced by accelerated charges

2. a charged particle oscillating about an equilibrium position is an accelerating charged particle.

antenna

3. PLASMA - highly ionized gas (a fourth state of matter) - the atoms are nearly all fully ionized and the substance consists of electrons and atomic nuclei (or positive ions)- "bremsstrahlung“: the electrons are accelerated, and the gas cloud emits radiation continuously. Some sources of free-free emission include ionized gas near star-forming regions or Active Galactic Nuclei (AGN).

How fast does it go?• The speed of the wave is the speed of energy transfer and is not

the same as the speed of the particle of the medium oscillating around equilibrium position.

The wave speed is determined by: ● the stiffness of the material more stiff higher speed each segment of medium is in tighter contact with its neighbor ● density - more difficult to change the velocity of larger masses than smaller ones greater density more inertia lower speed

How fast is transverse wave in strings? The wave speed in strings is determined by: ● the tension in the string

more tension higher speed ● the mass per unit length of the string (whether it’s a heavy rope or a light rope) thicker rope lower speed

L/m

Tv

As far as waves are concerned, the difference between steel and air is that steel is stiffer and denser than air. But the stiffness of steel is much greater than that of air, even though the density of steel is greater. Consequently, the stiffness factor influences the wave speed more and waves travel much faster in steel than in air.

Speed of sound in:

air: 343 m/s helium: 1005 m/s water: 1500 m/s bone: 3000 m/s steel rod: 5000 m/s glass: 4500 m/s

Waves in a violin string: A-string: 288 m/s, G-string: 128 m/s

Why do waves travel faster in steel than in air? 

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The speed of transverse waves in solids are about 0.6 times the speed of longitudinal waves in solids.

The speed of transverse waves in solids are about 0.6 times the speed of longitudinal waves in solids.

Transverse waves cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave.

Transverse waves cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave.

The earth is shaking

earthquakes

Earthquakes produce both longitudinal waves(called “P” waves – primary - faster – the first to be detected by seismologists) and

transverse waves(called “S” waves – secondary - slower – the second to be detected by seismologists)more destructive.

Definitions associated with waves

Amplitude, A

● is the maximum displacement of a particle from its equilibrium position. ● It is also equal to the maximum displacement of the source that produces the wave. ● From SHM, energy of a wave ∞ A2. If the wave doesn’t lose any of its energy its amplitude is constant.

Period, T ● is the time that it takes a particle to make one complete oscillation. ● is the time taken for one complete wave to pass any given point.Frequency, f

● is the number of oscillations made by a particle per second. ● 50 Hz means 50 oscillations per second

1 1f = T =

T f

Wave speed, v

● The speed at which wavefronts pass a stationary observer. ● It is constant, depending on the medium only.

Intensity, I

● The energy that a wave transports per unit time across unit area of the medium through which it is travelling is called the intensity. ● Intensity of a wave is the power per unit area that is received by observer. ● The unit is W/m2. ● Hence for a wave of amplitude A, we have that I ∞ A2

Wavelength, λ

● This is the distance along the medium between two successive particles that have the same displacement (that are in phase) (e.g. from crest to crest, or from compression to compression)

Transverse wave: displacement vs. x, Longitudinal wave: density vs. x or pressure vs. x

A displacement vs. position graph shows the displacement of all points along the wave. A snapshot of a wave at one instant of time.

A displacement vs. time graph shows the oscillations of one point on the wave. All other points will oscillate in a similar manner, but they will not start their oscillations at exactly the same time.

Transverse wave: displacement vs. t, Longitudinal wave: density vs. t or pressure vs. t

clever koala finds the speed of the wave to be: v = 2 m/s

Koala measures time between crests to be 0.5 s.

Koala measures distance between crests to be 1m.

Wave Equation

This applies to all waves water waves, waves on strings, sound waves, radio, light . .

distance wavelengthwave speed = = = wavelength frequency

time period

λv = = λf

T

Waves with different frequncies and wavelength will have the same speed in one medium, determined by that medium. If you shake the string faster (greater freq.) the wavelength will be smaller and vice versa

A sound wave produced by a clock chime is heard 515 m away 1.5 s later.

(a)What is the speed of sound in the air there? (b) The sound wave has a frequency of 436 Hz.

What is the period of the wave?

(c) What is the wave's wavelength?

(a) v = d/t = 515/1.5 = 343 m/s

(b) f = 1/T = 1/436 = 2.29x10-3 s

(c) v = f → = v / f = 0.87 m

A hiker shouts toward a vertical cliff 465 m away. The echo is heard 2.75 s later. (a) What is the speed of sound in air there? (b) The wavelength of the sound is 0.75 m. What is the frequency of the wave? (c) What is its period?

(b) v = f → f = v/ = 338/0.75 = 451 Hz

(a) v = distance/time = 2d/t = 2·465/2.75 = 338 m/s

(c) T = 1/f = 2.22x10-3 s

If you wanted to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency?

v = f v depends only on the medium. Therefore for given medium it is constant. So if wavelength increases the frequency decreases. You should shake it at lower frequencies. CHECK IT, PLEASE

A stone is thrown onto a still water surface and creates a wave. A small floating cork 1.0 m away from the impact point has the following displacement—time graph (time is measured from the instant the stone hits the water):

Find (a) amplitude (b) the speed of the wave (c) the freq. (d) wavelength

(a) A = 2 cm

(b) v = d/t = 1/1.5 = 0.67 m/s

(c) f = 1/T = 1/0.3 = 3.33 Hz

(d) λ = v/f = 0.666/3.333 = 0.2 m

plane waves: far away from the source circular wavefronts become straight lines

Wavefronts propagating from a point source

wavefront is the locus of points having the same phase. Set of points with the same displacement from equilibrium position and the same velocity vector.

Ray - direction of wavedirection of energy transfer

EM waves striking the earth are plane waves

Electromagnetic waves – Electromagnetic spectrum

● Visible light is one part of a much larger spectrum of similar waves that are all electromagnetic.

● EM waves are produced/generated by accelerated charges.

● EM wave is made up of changing electric and magnetic fields.

● The electric and magnetic field components of EM wave are perpendicular to each other and also perpendicular to the direction of wave propagation – hence EM waves are transverse waves.

● They all travel travel through vacuum with the same speed – speed of light c:

c = 2.99 792 458 x 108 m / s c ≈ 3 x 108 m/s

● This speed is completely independent of the frequency or the wavelength of the wave!!

● EM waves are waves, so: c = λf● greater λ smaller f

● This is a large speed ≈ 186,000 mi/s. If the beam of light could curve it would travel around the world about seven times in a single second.

● On the other hand, when one recalls that the nearest major galaxy to our own, the Andromeda galaxy, is about 2.9 million light years away, meaning that it takes 2.9 milion years for the light to reach the earth, the speed of light doesn’t appear so great after all.

● Although all EM waves are identical in their nature, they have very different properties, due to different wavelengths and frequencies, and therefore energy that they carry along.

● The energy of a wave is directly proportional to its frequency, but inversely proportional to its wavelength. In other words, the greater the energy, the larger the frequency and the shorter (smaller) the wavelength. Short wavelengths are more energetic than long wavelengths.

Electromagnetic waves – Electromagnetic spectrum

What is the origin of sound?

Vibrations of objects - a string, a reed, vocal cords, earthquake

• The vibration of the fork causes the air near it to vibrate

• Longitudinal wave – air molecules vibrate to and fro along direction of wave

How does sound travel in air?

• Analogy with opening and shutting a door periodically:

Open door inward: a compression travels across room (via molecules pushing neighbors)Close door: a rarefaction travels across room – some molecs are pushed out of room so leave lower pressure behind. Swing door open and shut periodically – get periodic compression-rarefaction wave across the room.

• Tuning fork – is exactly this action on a smaller, faster scale: prong vibrating is like the door opening and shutting.

• Radio loudspeaker – cone that vibrates in synch with electric signal, causing neighboring air molecules to vibrate …eventually sound wave filling the room

The pressure waves make your eardrum vibrate

frequency of sound waves = pitchHigh pitch – high frequency (a piccolo), whereas low pitch means low frequency (fog horn)

Frequencies of the Sound

• Human ear can hear between 20 – 20 000 Hz.• Infrasonic – below 20 Hz • Ultrasonic – above 20 000 Hz

Dogs can detect freq as low as 50 Hz and as high as 45,000 Hz while Cats detect freq between 45 Hz and 85,000 Hz. Bats who rely on reflection of sounds that they emit for navigation can detect freq as high as 120,000 Hz. Dolphins can detect freq as high as 200,000 Hz. Infrasound and sound in a range of 5 Hz to 10,000 Hz can be detected by elephants.

Low and high freq have the same speed. Higher freq waves have smaller wavelength, and lower freq waves have longer wavelengths since product λf = v is same.

• Speed of the sound depends of course on the medium.

• Air at 20 C: 343 m/s = 767 mph 1/5 mile/sec

• increases with temperature, humidity, right wind

Speed of sound in air

Speed does not depend on loudness (amplitude), nor on pitch (freq).

Autofocusing cameras emit a pulse of very high frequency (ultrasonic) sound that travels to the object being photographed, and include a sensor that detect the returning reflected sound. Calculate the travel time of the pulse for an object (a) 1.0 m away (b) 20 m away. Temperature is 200.

v = 343 m/s

a) d = 2 m d = vt, t = d/v t = 0.006 s = 6 ms

b) d = 40 m d = vt, t = d/v t = 0.15 s = 150 ms

• we see lightning before we hear thunder• we see a distant tree fall to the ground before we hear the thud…

v 1/3 km/s → 3 seconds rule: 3 s delay in the arrival of thunder after lightening correspond to a distance of 1 kmv 1/5 mi/s → 5 seconds rule : 5 s delay for every mile.

• speed of light is a million times as greatThe light from a lightning flash reaches us almost instantaneously; the corresponding sound wave, generated by heated expanding air near the lightning bolt, travels toward us at about 340 m/s.

• Sound pressure waves in a solid, liquid or gas

Sound travels in other media too• Through anything that is elastic i.e able to

change shape in response to an applied force and then resume its original shape once force is removed.

• putty is not elastic but steel is

Sound generally travels fastest in solids, then in liquids, and slowest in gasesair at 20 C: 343 m/s, 4x as fast in water, 15x as fast in steel

Also, generally less dissipation (ie fading away) in solids and liquids than in air,

• Can hear a distant train coming more clearly and sooner if put ear against the rail

• Motors of boats –or fingernails clicking - sound much louder to someone under water, than to someone above.

Sound needs a medium – won’t travel in a vacuum since nothing to compress and expand

Sound travels through rock at 3000 m/s, and through air at 340 m/s. If the munitions plant is 1 km away, calculate the time interval between the tremor waking the person and him hearing it through the air.

d = vt , so t = d/v

So time through rock = (1000m)/(3000 m/s) = 0.33 s

Time through air = (1000 m)/(340 m/s) = 2.94 s

So time interval = 2.94 -0.33 = 2.6 s

Some people claim they have an extra-sensory perception, citing the fact that they awaken from a deep sleep for no reason, get out of bed and walk to the window just in time to hear explosions from a distant munitions plant.Premonition ??Actually this can be explained by comparing the speed of sound through earth and through air! Assume the tremor of the sound wave traveling through earth awoke the person, who then walked to the window just in time to hear the sound wave traveling through the air.

That’s why dogs sleep on their ears.

Infrasonic sound f < 20 Hz Sources of infrasonic waves include earthquakes, thunder, volcanoes, and waves produced by vibrating heavy machinery. This last source can be particularly troublesome to workers, for infrasonic waves – even though inaudible – can cause damage to the human body. These low freq waves act in a resonant fashion, causing considerable motion and irritation of internal organs of the body.Infrasound is used in the nature for communication: elephants (~ 15Hz) couple of kilometers, whales – as sound travels faster in water (v ~ 1500 m/s) than in air, the call can be heard over distances of thousands kilometers.

Ultrasonic sound f > 20 kHz

Ultrasound is used for echolocation: dolphins, bats, sonar, sonograms Sonar appeared in the animal kingdom long before it was developed by human engineers.

So when ultrasound is emitted toward obstacle it will be reflected back and detected.

dolphins, ocras, whales

The ultrasound bats typically chirp is ~ 50 000 Hz. What is wavelength of that sound? The speed of sound wave in air is ~ 340 m/s.

v = lf so l = v/f l = 0.0068 m = 0.7 cm

So, bats use ultrasonic waves with l smaller than the dimensions of their prey (moth – couple of centimeters).

To echolocate an object one must have both emitter and detector. If the wavelength of an emitted wave is smaller than the obstacle which it encounters, the wave is not able to diffract around the obstacle, instead the wave reflects off the obstacle. Reflected wave is caught by detector giving it information on how far (2d = vt) and how big is the object (reflection from different directions)

Ships use SONAR to determine the depth of water they are in.

By timing how long the echo takes to come back and knowing the speed of sound in water, the depth can be calculated

The transmitter emits pulse, receiver detects reflected pulse.

SONAR (sound navigation ranging):

Why do I sound funny whenI breath helium?

• Sound travels twice as fast in helium, because helium is lighter than air

• Remember the golden rule v = • The wavelength of the sound waves you make with

your voice is fixed by the size of your mouth and throat cavity.

• Since is fixed and v is higher in He, the frequencies of your sounds is twice as high in helium!

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