3. In tranverse waves the motion of the disturbance is perpendicular to the direction of motion of the wave.

Longitudinal waves propagate in the same direction as the motion of the disturbance of the medium.

The particles of surface waves move in a circular fashion, up and down, back and forth, as the wave passes through.

5. A wave pulse is a single disturbance, a continuous wave has a constant source for the disturbance which creates it.

20. The nodes be touched without disturbing the motion of the wave.

32. f = 0.1 Hz. T = 1/f = 1/(0.1/sec) = 10 sec.

33. = 10m. T = 2s f = 1/T = 1/2sec = 0.5/sec. v = fsec)(10m) = 5m/sec.

p. 34438,40,43,45

Wave VideosReflection off a sea wall: http://www.youtube.com/watch?v=PevRZAxDxZwBig wave at beach: http://www.weather.com/blog/weather/8_21326.htmlhttps://www.youtube.com/watch?v=QdoTdG_VNV4&feature=player_embedded#at=131Tacoma narrows bridge: http://video.search.yahoo.com/search/video;_ylt=A2KLqIGXaSdPEn0AIxT7w8QF?p=tacoma+narrows+bridge&b=21&tnr=20

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=14&cad=rja&uact=8&ved=0CJEBEBYwDQ&url=http%3A%2F%2Fwww.joe.ie%2Fnews%2Fcurrent-affairs%2Fvideo-these-huge-waves-forced-pedestrians-to-flee-the-footpath-in-tramore-this-morning%2F&ei=YrZVU5GrFJCnsATLxYDYDw&usg=AFQjCNEee0VBKDWk-FqbGCzim6T6AgEF0g&sig2=WGLREQeIb59HyB3EiTcpJA

Standing Waves in Musical Instruments Resonance: Stringed instruments, such as

the guitar, piano or violin, and horn and wind instruments such as the trumpet, oboe, flute and clarinet all form standing waves when a note is being played. The standing waves are of either the type that are

found on a string, or in an air column (open or closed).

These standing waves all occur at natural frequencies, also known as resonant frequencies, associated with the instrument.

Standing waves

• Two similar periodic waves traveling in opposite directions form a standing wave.

Standing Wave Characteristics

While a standing wave does not travel itself, it is comprised of two waves traveling in opposite directions. Harmonic: The series of frequencies where

standing waves recur (1f, 2f, 3f,…). Where the first frequency is called the first harmonic (1f), the second frequency is called the second harmonic (2f), and so on.

The first harmonic = the first fundamental frequency (n = 1).

Overtones: The harmonic frequency + 1.

Harmonics and Overtones of Standing Waves

www.cnx.rice.edu

Standing Wave Characteristics (cont.) The time for one wave to travel to

the barrier and back is:

T = 2L/v

For a string fixed at both ends with n antinodes:

fn = n(v/2L) n = 1, 2, 3, …

Each fn represents a natural or resonant frequency of the string.

This relationship can be rewritten for as follows.

= 2L/n

www.electron4.phys.utk.edu

www.cord.edu

Longitudinal Standing Waves Wind instruments, such as the flute, oboe,

clarinet, trumpet, etc. develop longitudinal standing waves. They are a column of air. May be open at one or both ends. Wave will reflect back regardless as to whether or not it

is open or close ended.

Longitudinal Standing Waves – Open Tube In an open tube instrument like the flute, the

harmonics follow the following relationship:

fn = n(v/2L) n = 1, 2, 3, …

www.cnx.rice.edu

Longitudinal Standing Wave Applet

Longitudinal Standing Waves –Tube Closed on One End

In a closed tube instrument like the clarinet or oboe, the harmonics follow the following relationship:

fn = n(v/4L) n = 1, 3, 5, …

www.cnx.rice.edu

How does a string make music?

•What does a string look like when vibrating?

How do I measure

AmplitudeWavelengthFrequencyPeriod

For each of these?

L = /2

V = nf/2L

Key Ideas Sound waves are generated by a vibrating object

such as the string on a violin, your vocal chords or the diaphragm of a loudspeaker.

Sound waves can be transmitted through gases, liquids and solids.

If there is no medium, there is no sound. Sound is generated by the cyclical collisions of

atoms and molecules. Condensation and rarefaction denote portions of

the wave that are of slightly higher and lower pressure, respectively.

Key Ideas Sound waves travel at different speeds in

different mediums. They speed up when going from air to a liquid to a

solid. Pure tone is sound of a single frequency. Pitch and loudness are characteristics of sound

that represent its frequency and amplitude, respectively.

When two sound waves overlap slightly due to mildly different frequencies, they generate a beat.

Harmonics occur at multiples of the natural frequency.

Sound Waves

How is Sound Transmitted? Sound is created by

the cyclical collisions of atoms and molecules such that it is transmitted through the bulk matter.

www.library.thinkquest.org

Sound Wave Characteristics Condensation or Compression: Region of the

wave where air pressure is slightly higher. Rarefaction: Region of the air wave where the

pressure is slightly lower. Pure Tone: A sound wave with a single frequency. Pitch: An objective property of sound associated with

frequency. Pitch High frequency = high pitch. Low frequency = low pitch.

Loudness: The attribute of sound that is associated with the amplitude of the wave.

Beat: When two sound waves overlap with a slightly different frequency. Beats

Speed of Sound Speed of sound depends on the medium through which it

travels.

kT

m

Where:

k = Boltzman’s constant (1.38 x 10-23 J/K)

= Cp/Cv (~5/3 for ideal monotonic gases)

T = Temperature (K)

m = Average mass of air (~28.9 amu)

Air Water Steel

Speed (m/s) 343 1482 5960

vrms =

Doppler Shift The change in sound frequency due

to the relative motion of either the source or the detector.

High Pitched Sound

Low Pitched Sound

www.physicsclassroom.com

The Doppler Effect

http://www.youtube.com/watch?v=imoxDcn2Sgo

http://www.youtube.com/watch?v=a3RfULw7aAY

http://www.youtube.com/watch?v=19_727LxYDw

Doppler This demo shows the Doppler effect in action Doppler

Waves: Take 2

Mr. Davis

Review: Key characteristics of waves

Period (if axis is time)

Amplitude: The height of the wave from node to antinode (transverse waves), or the pressure in a compressive wave. Measured in units describing the wave

Frequency: The rate of occurrence of the wave (in Hertz or cycles / second)

Wavelength: The distance traversed by a full cycle of the wave Node: The “zero point” of the waveAntinode: The extreme point of the wave (max or min amplitude)Period: The time between successive waves

The frequency

f = 1/T

where T is the period.

All of these terms are required for the Regents

What happens when two waves collide?

They pass through each other without changing and keep on going.(Have you ever crossed the beams of two flashlights to see what would happen?)

Series 1

-1.5

-1

-0.5

0

0.5

1

1.5

1 62 123 184 245 306 367 428 489 550 611 672 733 794

Series 1

-1.5

-1

-0.5

0

0.5

1

1.5

1 62 123 184 245 306 367 428 489 550 611 672 733 794

Series 1

Series 2

-1.5

-1

-0.5

0

0.5

1

1.5

1 48 95 142 189 236 283 330 377 424 471 518 565 612 659 706 753

Series 1

Series 2

Series 1+2

-1.5

-1

-0.5

0

0.5

1

1.5

1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691 737 783

                                   (7)

Fundamental Frequency and Harmonics

Two waves of similar frequency

Beat frequency is the difference between them

Beat Frequency

Surface Waves

Surface Wave

A wave that has characteristics of both transverse and longitudinal waves (Ocean Waves).

Surface Wave Applet

Surface Waves

Thus far, you have seen the profile view of waves. How do these waves look from above?

= Wavelength

Direction of propagation

Wavefronts

Reflection of Surface Waves The law of reflection states that the angle of

incidence is equal to the angle of reflection.

Wave Crest

i = r

Reflected Ray

Incident Ray

r

Normal

i

Refraction of Surface Waves If the direction of the wave changes, then

the wave is said to have refracted. Refraction.

Refraction of Surface Waves

When surface waves move from deep water to shallower water: The wavelength decreases. The amplitude increases. The speed decreases.

Why? Because of interactions with the bottom.

Note: The frequency does not change!

Interference As per the principle of linear superposition:

Crests will combine with crests and troughs will combine with troughs in a constructive manner.

Where a crest meets a trough, interference will be totally destructive.

Destructive Interference

Constructive Interference

Diffraction When a wave front is incident on a barrier with

an opening, the wave will spread out after crossing the barrier. This process is called diffraction.

As the slit becomes narrower,the amount of diffraction will increase.

As the wavelength increases,the amount of diffraction increases.

Wavelength, frequency, andhence velocity, do not change.

Diffraction

Key Ideas Surface waves have characteristics of both

transverse and longitudinal waves. Waves transfer energy without transferring

matter. Waves can interfere with one another resulting

in constructive or destructive interference. The law of reflection states that angle of incident

wave equals the angle of the reflected wave. Diffraction is the spreading out of a wave when it

encounters a barrier.

Law of Reflection The angle of incidence with respect to the

normal is equal to the angle of reflection.

www.sol.sci.uop.eduwww.sol.sci.uop.edu