Wave MotionThink of yourself in the ocean…When you are far out beyond the breaking

of the waves, which way do you move when a wave goes by and you are floating?

The velocity of a wave, and particles within the wave, are different in magnitude and direction.

Waves will move along the surface of the water, the water particles will move up and down in the same spot.

What are waves?Waves carry energy from one place to

another. Example, the energy given by my hand to the

long spring causes a wave to carry that energy to the other end.

A rock thrown into a still pond will give energy to the water and cause a wave to be formed.

Wave “pulse”With a quick upward movement of a hand on

the end of a rope (or spring)…Causes the rope to go upwards, it will flow

along the rope, but the end where the movement began goes back to the same position.

(Ignore b for now)

Continuous or Periodic waveInstead of having one disturbance on the end

of the rope, what if I have a continuous disturbance?

The disturbances are called vibrations. If the vibration is in SHM, then the wave itself

will be sinusoidal in both space and in time. space: the wave will always look like either a

sine or cosine function.Time: the wave will look like SHM over a long

period of time.

Describing wavesAmplitude: The maximum height of the crest,

or depth of a trough, from an equilibrium point.

Wavelength: The distance between two successive crests or two successive troughs (λ – lambda)

Frequency: the number of crests that pass a given point per unit of time. (a full cycle).This is the inverse of the period (time for one

cycle).

Parts of a wave

Wave velocityThe velocity of a wave is the distance of one

wavelength in one period. Thus the wave velocity is lambda/T.Since 1/T = f…

v = λf

Types of wavesTransverse wave: The particles of the

medium in which the wave travels through move perpendicular (transverse) to the motion of the wave.

Longitudinal waves: The vibrations of the particles in the medium are along the same direction as the motion of the wave. The wave compresses and expands.

http://paws.kettering.edu/~drussell/Demos/waves/wavemotion.html

Energy transported by wavesRemember from SHM, E = ½ k A2

Therefore, energy transported by a wave is proportional to the square of the amplitude.

Intensity of a waveIntensity is defined as Power/Area.

So… I = (energy/time)/area, and energy is proportional to the amplitude squared…

Intensity is proportional to the amplitude squared.

Intensity continued…We will be talking about waves that are

spherical, so surface area of a spherical wave (from geometry) is 4πr2

So if I = Power/Area, or I = Power/ 4πr2, Then Intensity is in proportion to the inverse

square of the distance. (think butter gun)

Sound WavesThree things to know about sound waves:1)There must be a source for a sound wave,

that source will be a vibrating object.2)The energy transferred from the source is

longitudinal.3)The sound is detected by an ear or an

instrument.

Characteristics of Sound wavesSound can travel in different materials

besides for air. In air, the speed of sound is 343 m/s.

More characteristicsPitch: high or low sounds (like a flute

compared to a tuba).The lower the frequency the lower the pitch.The audible range is between 20Hz and

20,000Hz for healthy hearing.As a person gets older, the high-frequency

limit lowers to about 10,000Hz.Frequencies above 20,000 Hz is called

ultrasonic (different from supersonic)

UltrasonicMany animals can hear ultrasonic

frequencies.Dogs can hear up to 50,000 Hz, and bats

100,000 Hz. Autofocus cameras emit a pulse of ultrasonic

sound that travels to the object being photographed and back to the camera.

A sensor times the reflected sound to know how far the object is.

InfrasonicSound waves that are below the audible

range (20Hz)Earthquakes, thunder, volcanoes, and waves

produced by vibrating heavy machinery can produce infrasonic waves.

Infrasonic waves, like ones that can be produced by heavy machinery can harm the human body.

Characteristics of soundLoudness: This is the intensity of the sound

wave.As stated earlier, intensity varies with the

inverse square of the distance. The human ear can detect sounds with an

intensity as low as 10-12 W/m^2 and as loud as 1 W/m^2 (larger will cause pain)

This is a huge range…

Alexander Graham BellUsed a logarithmic scale to measure the

intensity of a sound. We call this unit of measurement a Bel (or more commonly a decibel, 10 dB = 1 bel).

Beta is measured in dB, and I0 is a reference level, which will be the lowest intensity we can hear (1x10^-12

Example…

0

log10I

I

Doppler Effect

Doppler effectAs an object that emits a sound is moving

towards an observer, the frequency of the sound increases.

As an object that emits sound is moving away from an observer, the frequency of the sound decreases.

The Doppler effect has applications with sound, but will also have applications next week when we discuss light waves in more detail.

Sonic BoomsWhen an object is moving faster than the

speed of sound, it is said to have reached supersonic speed.

An object moving faster than the speed of sound has “outrun” its sound waves.

http://library.thinkquest.org/19537/

Day 2: Reflection and Interference

Reflection

ReflectionIf the end of a cord is free to move, the pulse

will reflect on the same side of the cord as it is sent.

If the end of the cord is fixed, then the pulse will comeback inverted from the way it is sent.

This is due to Newton’s Third Law

Law of ReflectionThe angle of reflection equals the angle of

incidence.

InterferenceWhen two waves pass through the same

region of space at the same time.Principle of Superposition

The region where waves overlap, the resultant is the algebraic sum of their separate displacements.

This could be constructive or destructive interference.

Interference

Phases and interference for continuous wavesFor constructive interference to occur, waves

are said to be “in phase”.For destructive interference to occur, waves

are said to be “out of phase”

Sound “beats” and interferenceWhen two sounds (or more) of different

frequencies are played at the same time, there is both constructive and destructive interference.

This causes a “beat”.http://library.thinkquest.org/19537/java/Beats

.htmlhttp://www.lon-capa.org/~mmp/applist/beats/

b.htmAnd the best for last…http://www.falstad.com/interference/

Standing wavesIf you have a fixed end of a cord and you can

vibrate it at a certain frequency so it just looks like it is oscillating up and down without traveling down the cord, this is called a standing wave.

Places where there is complete destructive interference are called nodes, and places where there is constructive interference are called anti-nodes.

ResonanceFrequencies at which standing waves are

produced are called “natural frequencies” or “resonant frequencies”.

Resonance occurs because everything in nature has a natural frequency. In vibrating objects, there is only one resonant frequency.

If this frequency is hit, then it causes the amplitude of the wave to increase… sometimes catastrophically.

Resonance in cordsCords are different because they have many

natural resonant frequencies. Each of which is a whole-number multiple of the lowest resonant frequency.

HarmonicsFirst, notice that the different resonant

frequency depends on the length of the cord.The lowest frequency, the fundamental

frequency, corresponds to one half of a wavelength, L = 1/2λ1.

When a frequency is an integral multiple of the fundamental frequency, they are called harmonics.

The fundamental frequency is the first harmonic

Other harmonicsThe second harmonic is now one full

wavelength, or L = 1λ. The third harmonic is now 1.5

wavelengths, or L = 3/2λIn total…

Or solving for lambda

And since f = v/λ…

2nnL

n

Ln

2

12nf

L

nvvf

nn

Sounds by air columnsFirst, let us examine an instrument such as a

flute, also known as an “open tube”.Just like the string situation, we will look at

the number of wavelengths for each overtone.

12nf

L

nvvf

nn

Closed tubeAn example of a closed tube could be a

clarinet, there is always a displacement node at the closed end, because the air is not free to move, and an anti-node at the open end.

We will see in a moment, that this means that the fundamental frequency frequency will be L = ¼ λ.

We will also see, that there is no way for the even harmonics to exist, but only odd harmonics.

...7,5,3,11

n

nffn4

1L