Conceptual Physics Chapter 251 Chapter 25 Waves. Conceptual Physics Chapter 252 Vibration of a...

Conceptual Physics Chapter 25

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Chapter 25 WavesChapter 25 Waves


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Vibration of a PendulumVibration of a Pendulum

¤ The back-and-forth motion of a pendulum demonstrates a vibration.

¤ The time to complete one back-and-forth motion is called the period, T. The period is usually measured in seconds.

¤ The frequency, f, is a measure of how often the pendulum swings back and forth and is measured in cycles per second or Hertz (Hz).


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Vibration of a PendulumVibration of a Pendulum

¤ The period is not dependanton the mass of the pendulumnor is it dependant on theinitial amplitude.

¤ The period is only dependant on the length of the pendulum and the acceleration of gravity.

g

LT = 2π


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QuestionQuestion

A pendulum completes five back-and-forth cycles in 15 seconds.What is the period of the pendulum?What is the frequency of the pendulum?


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Sine WaveSine Wave

¤ A sine wave can be created from the simple harmonic motion of a mass attached to a spring.

¤ The high points are called crests and the low points are called troughs.

crests

troughs

¤ The amplitude, A, is the vertical distance from the equilibrium, or home position, to the crest or trough.

¤ The wavelength, λ, is the distance between successive identical parts on the wave.


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Energy Transfer by WavesEnergy Transfer by Waves

¤ Waves are a disturbance that travel through a medium.

¤ The source of all waves is something that vibrates.

¤ The wave carries energy away from the source.

¤ The disturbance moves along the medium; the medium itself does not move.

¤ The energy associated with the wave is dependant on the amplitude of the wave.


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Classification of WavesClassification of Waves

¤ All waves can be classified as either mechanical waves or electromagnetic waves.

¤ Mechanical waves rely on a material medium in which to propagate. E.g., sound waves, water waves, slinky waves.

¤ Electromagnetic waves are able to transmit energy through empty space. E.g., light waves, radio waves, microwaves, X-rays.

¤ Our focus in this chapter will be on mechanical waves.


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Classification of WavesClassification of Waves

¤ Another way to classify waves is on the basis of the direction of movement of the individual particles of the medium relative to the direction in which the waves travel.

¤ Three notable categories are transverse waves, longitudinal waves and surface waves.


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Transverse WavesTransverse Waves

In a transverse wave the particle displacement is perpendicular to the direction of wave propagation.

direction of wave travel

direction of particle motion

The wave propagates from left to rightwhile the particles simply oscillate up and down – the particles do not travel with the wave!


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Longitudinal WavesLongitudinal Waves

In a longitudinal wave the particle displacement is parallel to the direction of wave propagation.

direction of wave travel

direction of particle motion

The wave propagates from left to rightwhile the particles oscillate back and forth about their equilibrium positions


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Slinky WavesSlinky Waves

A slinky can be used to produce either a longitudinal wave or a transverse wave.


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Surface WavesSurface Waves

Surface waves are a combination of both longitudinal and transverse waves.

As a water wave propagates from left to right across the surface of the water, the particles move in clockwise circles. The radius of the circles decreases at greater depths beneath the surface.


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Wave SpeedWave Speed

If we count the number of wave crests that pass the bird each second (the frequency) and observe the distance between successive crests (the wavelength) we can find the horizontal distance the waves move each second (the wave speed).

v = fλ¤ The speed of the wave is dependant

solely on the medium through which the wave travels.

¤ The frequency of the waves is an inherent property of the waves and is dictated by the device or event that generates the wave

¤ If the frequency is increased, the wavelength will be reduced proportionately while the wave speed remains constant!


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InterferenceInterference

¤ Unlike matter, multiple waves can occupy the same space at the same time.

¤ When waves interact, they generate interference patterns.

¤ Within the pattern, wave effects may be increased, decreased or neutralized.


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¤ When the waves are in phase (crest matches with crest), the waves undergo constructive interference and reinforce one another.

¤ When the waves are out of phase (crest matches with trough), the waves undergo destructive interference and partially or fully cancel one another.

¤ Regardless, the interference pattern is temporary. The waves pass through one another with no permanent effect to their amplitude, wavelength, frequency or speed.

Run Simulation

http://www.surendranath.org/Applets/Waves/Twave02/Twave02Applet.html


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¤ Interference patterns can develop when water waves pass through one another. Notice the regions of alternating constructive and destructive interference.


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Standing WavesStanding Waves

¤ A standing wave can be produced as a result of interference between two waves of equal amplitude and wavelength passing through one another.

¤ In a standing wave, the nodes result from destructive interference. These nodes remain stationary.

¤ The antinodes are points of maximum displacement which result from constructive interference.

¤ Nodes are always separated byone-half wavelength.

Run Simulation

http://www2.biglobe.ne.jp/~norimari/science/JavaEd/e-wave4.html


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Standing WavesStanding Waves

¤ Different modes of vibration can be produced in the same medium under different conditions.

The easiest standing wave to produce has one segment.Shaking the rope with twice the frequency will produce a standing wave with two segments.

Shaking the rope with three times the frequency will produce a standing wave with three segments.


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The Doppler EffectThe Doppler Effect

¤ The Doppler effect is observed when a wave source is moving relative to the observer of the waves.

¤ There is an apparent upward shift in frequency for observers towards whom the source is approaching.

¤ There is an apparent downward shift in frequency for observers from whom the source is receding.

¤ The Doppler effect can be observed for any type of wave - water wave, sound wave, light wave, etc.


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¤ A bug bobbing up and down in the middle of a quiet pond produces circular waves that travel outward in all directions. The wave fronts form concentric circles of increasing radius.¤ Waves encounter point A as frequently as they encounter point B.

¤ The frequency at both points is equal to the bobbing frequency of the bug.


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¤ If the bug begins moving to the right, the wave fronts remain circular, but the pattern is distorted – the circular waves are no longer concentric.

¤ An observer at point B would now encounter the waves more frequently and an observer at point A would encounter the waves less frequently.


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The Doppler effect is evident when you hear the changing pitch of a fire truck’s siren as it passes you. When the fire truck approaches you, the waves encounter you more frequently and you hear a higher pitch. When the fire truck moves away from you, you hear a drop in pitch because the waves are encountering you less frequently.


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Bow WavesBow Waves

¤ When the speed of the source in a medium is as great as the speed of the waves it produces, the waves begin to pile up – a bow wave is formed.

¤ The faster the source moves, the narrower will be the V that is produced.


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Shock WavesShock Waves

¤ When a supersonic aircraft exceeds the speed of sound, three-dimensional spherical waves pile up and generate a conical shock wave.

¤ When this shock wave reaches an observer on the ground, a sonic boom is heard.


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Shock WavesShock Waves

A large cloud of condensation forms as this F – 18 Hornet breaks the sound barrier.

http://www.fas.org/man/dod-101/sys/ac/jet.mpeg

Conceptual Physics Chapter 251 Chapter 25 Waves. Conceptual Physics Chapter 252 Vibration of a...

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