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Wave Behavior
• Reflection• Refraction• Diffraction
• Interference• Doppler Effect
Boundary Behavior• A sound wave travelling through water reflects off the
submarine and returns to its original source. • Does reflection of a wave affect the speed of the wave?
• The behavior of a wave (or pulse) upon reaching the end of a medium is referred to as boundary behavior.
Fixed-end Reflection
• Rope is connected to a pole.• The last particle is fixed at position and unable
to move.
applet
applet
• When the incident pulse reaches the boundary:
Fixed-end Reflection
Reflected pulse in inverted
A portion of energy is transmitted to the pole
The disturbance returns to the source (left side)
• What happens to the wave characteristics?
1. Speed
2. Wavelength
3. Amplitude
Fixed-end Reflection
Remains the same
Remains the same
Decreases
Free-end Reflection
• Rope is attached to a loosely-fit ring around the pole.
• Last particle is free to move.
applet
• Reflected pulse is not inverted.
Free-end Reflection
Remains the same
Remains the same
Decreases
Speed
Wavelength
Amplitude
Reflection - Wave diagram
Law of reflection: angle i = angle r
Wavelength remains the same
λ
Wave diagram – wave frontsThese lines represent wave frontsWave fronts is a imaginary line that joins up particles of the same phase together.
Direction of wave. It is perpendicular to the wave fronts.
Wave diagram – wave fronts
All the particles along the wave fronts are in phase. All are “crests” of a transverse wave
Refraction
• Consider transmission of the rope wave from less dense medium ( the thin rope) towards the boundary with a more dense medium (the thick rope).
Refraction
wavelength frequency speed TypeReflected wave same same same inverted
Transmitted wave smaller same slower Same as source
Refraction – wave diagram applet
Video: ripple tank
Water waves travelling from less dense to denser medium:
Speed decreases
Frequency remains the same
wavelength decreases
Refraction – wave diagram
Incident wave direction
Refracted wave direction
Wavelength decreases as wave travels from less dense to denser medium.
Refraction – Beach Erosionanimation
headlandBay
shallowdeep
• During the day the air is warmest near the ground and cooler away from ground.
• Sound wave closest to the ground is fastest, and the wave farthest above the ground is travelling the slowest.
Refraction of Sound Day
Less dense medium
denser medium
Sound waves bends “towards the normal”
• Day time – sound bends upwards.• A "shadow zone" region created in which sound wave cannot
penetrate. • Person standing in the shadow zone will not hear the sound
even though he/she might be able to see the source
Refraction of Sound - Day
• During the night the air is cooler near the ground and warmer away from ground.
• Sound wave closest to the ground is slowest, and the wave farthest above the ground is travelling the fastest.
Refraction of Sound - Night
denser medium
Less dense medium
Sound waves bends “away the normal”
• Night time – sound bends downwards.
Refraction of Sound - Night
Loud Thunder?
Cooler air
warmer air
Interference
• two waves meet while travelling along the same medium.
• net effect of the two individual waves.
video
Constructive interference Destructive interference
Constructive Interference
• occurs at any location along the medium where the two interfering waves have a displacement in the same direction.
• as a result, the medium has a resultant displacement which is greater than the displacement of the two interfering pulses.
applet
Video: wave pool
• occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction.
• resultant displacement is either zero or smaller than the original displacement of both waves.
Destructive Interferenceapplet
Video: Microwave interference
After Interference?• Interestingly, the meeting of two waves along a medium does
not alter the individual waves or even deviate them from their path.
• two waves will meet, produce a resultant shape of the medium, and then continue on doing what they were doing before the interference.
Quiz 1• Several positions along the medium are labeled with a letter.
Categorize each labeled position along the medium as being a position where either constructive or destructive interference occurs.
ANSConstructive Interference:
G, J, M , N
Destructive Interference:
H , I , K , L , O
Quiz 2
• Jimmy and Johnny are both creating a series of circular waves by jiggling their legs in the water. The waves undergo interference and create the pattern represented in the diagram at the right. The thick lines in the diagram represent wave crests and the thin lines represent wave troughs. Several of positions in the water are labeled with a letter.
• Categorize each labeled position as being a position where either constructive or destructive interference occurs.
Quiz 2Constructive Interference:
A, B
Destructive Interference:
C,D,E,F
Standing Wave• A standing wave pattern results from the
interference of two or more waves along the same medium.
• All standing wave patterns are characterized by nodes.
applet
Standing Wave - Nodes• Nodes occur when two waves interfere such that one wave is
displaced upward the same amount that a second wave is displaced downward.
• Destructive interference leads to a point of "no displacement." A node is a point of no displacement.
Standing Wave - Antinodes• There are other points along the medium which undergo
vibrations between a large positive and and large negative displacement.
• These are the points which undergo the maximum displacement during each vibrational cycle of the standing wave. In a sense, these points are the opposite of nodes, and so they are called antinodes.
Standing Wave• Standing wave can only be obtained when the proper frequency is used,
such that the interference of the incident wave and the reflected wave produces specific points along the medium which appear to be standing still nodes and the antinodes
• nodes and antinodes are not actually part of a wave. Recall that a standing wave is not actually a wave but rather a pattern which results from the interference of two or more waves.
Natural Frequency• Nearly all objects, when hit or struck or plucked or strummed
or somehow disturbed, will vibrate. If you drop a stick or pencil on the floor, it will begin to vibrate.
• The frequency or frequencies at which an object tends to vibrate when disturbed is the natural frequency of the object.
Natural Frequency
The actual frequency is dependent upon :
1. the properties of the material the object is made of (this affects the speed of the wave)
2. length of the material (this effects the wavelength of the wave).
Video: singing glass
Video: unbelievable music
Forced Vibration
• Pluck a guitar string compared to the same string mounted on a guitar.
• What is the difference?
Much louder when string on the guitar is plucked. Why?
Forced Vibration• When the string is attached to the sound box of the guitar,
the vibrating string forces the sound box to vibrate at its natural frequency.
• The sound box in turn forces air particles inside the box to vibrate at the same natural frequency as the string.
Sound box
Forced Vibration
• The entire system (string, guitar, and enclosed air) vibrates and forces surrounding air particles into vibrational motion.
• The tendency of one object to force an adjoining object into vibrational motion is referred to as a forced vibration.
demo
• Video Demo
ResonanceVideo: motor resonance
Video: pendulum resonance
Video: ghost swing
Resonance
• Resonance occurs when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.
• Result of resonance is always a very large vibration.
Tacoma Narrows bridge Washington, 1940 video
• Plastic tube with air column
Resonance - Experiment
When the natural frequency of the air column is tuned to the frequency of the vibrating tuning fork, resonance occurs and a loud sound results.
Resonance occurs at odd multiples of /4ג . Why?
Resonance – Standing wave
• When an object is forced into resonance vibrations at one of its natural frequencies, it vibrates in a manner such that a standing wave is formed within the object.
• Such patterns are only created within the medium at specific frequencies of vibration. These frequencies are known as harmonic frequencies or merely harmonics.
Resonance – Sound waves
• Demo - Chladni plate, violin bow and salt
• Pattern formed is the standing wave pattern associated with one of the natural frequencies of the Chladni plate.
• Salt vibrate and tumble about the plate to reaches point along the plate which are not vibrating.(nodes)
Resonance – Sound waves
• Music and Harmonics
Resonance – Sound waves