Wave InteractionsWave behavior at boundaries

between different media

What happens?

It depends on the density of the various media...

If DA< DB then most of the incident wave’s energy will be reflected* AND the wave will be inverted upon reflection...

Notice that the frequency of both the reflected and transmitted ray are the same as the incident ray!

*Note that the intensity of the reflected and transmitted rays vary according to the angle of incidence as well. This will be discussed in significant detail during our study of visible optics.

When DA > DB ...

Note that the reflected wave is not inverted in this situation.

What happens when a wave impacts a boundary at an angle?

Law of Reflection: i = r

i r

Note that theangles are measured withrespect to thenormal, or perpendicularline at the boundary.

Interference (Superposition)• When two waves overlap and form a wave of

greater amplitude than the incident waves we have constructive interference.

• Destructive interference occurs when two waves of opposite (positive and negative) amplitudes interact producing a waveform of smaller amplitude than the originals.

• Sometime destructive interference can even completely cancel out an existing waveform. We use this principal in several important military and civilian applications...

Constructive Interference:

Notice that since both wave A and wave B have the same frequency as well as the same amplitude, the resultant waveformhas only twice the amplitude, but the same frequency.

Destructive Interference:

Since both waves A and B have the same amplitude but are exactly one-half wavelength out of phase, the wave signal is completely canceled out.

Note that these examples illustrate both of the extreme cases of interference.

Most interference is actually a combination of constructive and

destructive processes.

http://www.kettering.edu/~drussell/Demos/superposition/superposition.html

Diffraction:The “bending” of waves that encounter a sharp corner or edgeRipple tank diffractionhttp://www.youtube.com/watch?v=4EDr2YY9lyA&safety_mode=true&persist_safety_mode=1 Beach diffraction:http://www.youtube.com/watch?v=IZgYswtwlT8&safety_mode=true&persist_safety_mode=1 Beach diffraction w/ interference:http://www.youtube.com/watch?v=Zg2ClLspb8g&feature=related&safety_mode=true&persist_safety_mode=1 2 source interference in ripple tank:http://www.youtube.com/watch?v=5PmnaPvAvQY&feature=related&safety_mode=true&persist_safety_mode=1

Doppler Effect:• Waves produced from a stationary, non-

directional source move outwards in all directions at the same speed, like ripples from tossing a rock into a still pond.

• Assuming that a source is propagating in a forward direction waves produced by that moving source will “bunch up” in front of the source and “spread out” behind.

• This “bunching up” and “spreading out” can be measured by observing the frequency of the waves and thereby used to determine the velocity of the object producing the waves

Applications• Radar (weather and military)• Astronomy• Location of a sound source by pitch• http://www.youtube.com/watch?

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

t63xYSgmKE

Bow Waves

• Bow waves are produced when a moving object creates mechanical waves in the fluid it is traveling in by pushing that fluid in front of it. Although bow waves often take the form of transverse, “uppy-downy” waves, they are a good example of longitudinal mechanical waves.

• Examples include boats and airplanes

The sonic BOOM• As a plane flies the majority of the sound

produced by its passage is caused by its engines and is directed out the back of the plane (just like a speaker pointed backwards).

• However, the plane creates sound just by passing through the air and pushing air in front of it (bow waves).

• The sonic boom is created when the aircraft accelerates to a high enough velocity that it actually tears through the sound waves in the air in front of it.

• If you ever have the experience to hear a sonic boom (and I hope your ears are protected or that the aircraft is really far away) you will actually hear 2 bangs…sort of a ba-boom sound. What do you think causes this effect?

• An aircraft also creates a sonic boon when it decelerates to below Mach 1 (approx. 343 m/s depending on pressure and temperature of the air) as it rips backwards into its bow waves.

• Once the aircraft is traveling beyond the speed of sound a very cool effect happens:

The sound wave itself will be so far behind the aircraft that it may appear as though the sound has no source!

Resonance• Resonance is an extremely complicated

phenomena that occurs only under a combination of very specific circumstances.– These circumstances depend on the specific system.

• Resonance occurs when a standing wave is set up such that the media around and/or immediately adjacent to the wave begins to vibrate.

• The frequency at which this occurs is called the natural frequency of the medium.

What is a Standing Wave?• A standing wave is a wave that occurs in a media such

that some multiple wavelengths are present, vibrating in the medium.• A classic example is a closed or open tube pipe resonator

(although the type, closed or open affect the conditions under which the resonance will occur).– You will deal with an example of a closed tube resonator and

standing waves in your lab assignment.• Most wind or brass instruments and many percussion

instruments are close and/or open tube resonators, although string instruments utilize the same principles.

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Standing Waves and Resonance• Standing waves DO NOT cause resonance, but they are necessary for resonance to occur.

• Further information: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html

• A standing wave typically occurs when one or more ends of the medium in which the wave is traveling is anchored, thus forcing the wave to interact with this fixed point in space. The reflected wave creates a sequence of interference which amplifies and subsequently nullifies the waveform continually. http://www.walter-fendt.de/ph14e/stwaverefl.htm

• A standing wave often occurs when that fixed point is at any factor of ¼ of a wavelength* away from the source of the wave. When this occurs the “standing” wave often appears to be stationary within the medium.*Closed tube resonator or string wave with both ends fixed.

Typical Standing waves in a closed tube resonator:

http://cnx.org/content/m12413/latest/http://cnx.org/content/m12589/latest/

• Often, when a standing wave occurs, the medium and its surroundings will begin to vibrate in sync with the wave. This effect is what we call resonance or sympathetic vibration.

• Sometimes resonance can be desirable (i.e., music), but in some cases, the creation of vibration at an object’s natural frequency can have devastating effects. http://www.pbs.org/wgbh/nova/bridge/meetsusp.html

http://www.encyclomedia.com/video-tacoma_suspension_bridge_disaster.html

• More info: http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge

• Nikolae Tesla, a famous physicist who pioneered electric power transmission (AC power = waves) did a great deal of work with resonance, going so far as to devise equations that “proved” that the use of resonance could be used by humans as a destructive tool. However, reality showed that the human use of the resonance effect, the creation of sympathetic vibrations on a large scale is far more complicated than originally believed.

• Most large structures have a number of ways to rid themselves of excess kinetic energy naturally, via damping effects and friction, but sometimes, rarely, the right combination of conditions occur and rather than dampen kinetic energy, a resonance condition is built that amplifies a wave beyond the integrity of its transmission media, as you saw in the Tacoma-Narrows video.