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# p. 344 38,40,43,45 - PowerPoint PPT Presentation

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.

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## p. 344 38,40,43,45

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Presentation Transcript

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.
• A wave pulse is a single disturbance, a continuous wave has a constant source for the disturbance which creates it.
• The nodes be touched without disturbing the motion of the wave.
• f = 0.1 Hz. T = 1/f = 1/(0.1/sec) = 10 sec.
• 33. l = 10m. T = 2s  f = 1/T = 1/2sec = 0.5/sec. v = f l = (0.5/sec)(10m) = 5m/sec.

Wave Videos

Reflection off a sea wall: http://www.youtube.com/watch?v=PevRZAxDxZw

Big wave at beach: http://www.weather.com/blog/weather/8_21326.html

Tacoma narrows bridge: http://video.search.yahoo.com/search/video;_ylt=A2KLqIGXaSdPEn0AIxT7w8QF?p=tacoma+narrows+bridge&b=21&tnr=20

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.

www.electron4.phys.utk.edu

www.cord.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 fnrepresents a natural or resonant frequency of the string.
• This relationship can be rewritten for  as follows.

 = 2L/n

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.

www.cnx.rice.edu

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, …

• Longitudinal Standing Wave Applet

www.cnx.rice.edu

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, …

How does a string make music?

• What does a string look like when vibrating?

How do I measure

Amplitude

Wavelength

Frequency

Period

For each of these?

V = nf/2L

L = l/2

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

www.library.thinkquest.org

How is Sound Transmitted?
• Sound is created by the cyclical collisions of atoms and molecules such that it is transmitted through the bulk matter.
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

vrms =

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)

Low Pitched Sound

High Pitched Sound

www.physicsclassroom.com

Doppler Shift
• The change in sound frequency due to the relative motion of either the source or the detector.
The Doppler Effect

Doppler
• This demo shows the Doppler effect in action
• Doppler

### Waves: Take 2

Mr. Davis

Review: Key characteristics of waves

All of these terms are required for the Regents

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

Wavelength: The distance traversed by a full cycle of the wave

Node: The “zero point” of the wave

Antinode: The extreme point of the wave (max or min amplitude)

Period: The time between successive waves

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

The frequency

f = 1/T

where T is the period.

Period (if axis is time)

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?)

Beat Frequency

Two waves of similar frequency

Beat frequency is the difference between them

Fundamental Frequency and Harmonics

### Surface Waves

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

Wavefronts

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

Direction of propagation

l = Wavelength

r

i

Reflection of Surface Waves
• The law of reflection states that the angle of incidence is equal to the angle of reflection.

Wave Crest

Reflected Ray

Normal

i =r

Incident Ray

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!

Constructive Interference

Destructive Interference

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.
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, and

hence 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.