Ch 25 Vibrations & Waves
Images from Paul Hewitt and text from his book Conceptual Physics were used to create this page. Other sources are cited with image.
sine wave
sine curve- a curve whose shape represents the crests and troughs of a wave, as traced out by a swinging pendulum that drops a trail of sand over a moving conveyor belt. A sine curve is a pictoral representation of a wave.
sine wave labeled
A wave is a disturbance that repeats regularly in space & time that is transmitted progressively
from one place to the next with no actual transport of matter. The energy of the wave moves, not the medium.
crest- one of the places in a wave where the wave is highest or the disturbance is greatest
amplitude- the distance from the midpoint to the maximum (crest) of a wave or, equivalently, from the midpoint to the minimum (trough)
trough- one of the places in a wave where the wave is lowest, or the disturbance is greatest, in the opposite direction from a crest
wavelength- the distance from the top of the crest of a wave to the top of the following crest, or equivalently, the distance between successive identical parts of the wave
transverse wave

transverse wave- a wave with vibration at right angles to the direction the wave is traveling

Examples of Transverse waves: waves in the strings of instruments, waves on surfaces of liquids, and electromagnetic waves such as light & radio waves
 
tansvers and longitudinal waves
longitudinal wave- a wave in which the vibration is in the same direction as that in which the wave is traveling, rather than at right angles to it. The medium vibrates parallel to the direction of energy transfer. Sound waves & seismic waves are longitudinal waves.
Wave Behavior: Reflection
                                   
Law of Reflection: the angle of incidence = angle of reflection           The angle is created between incident ray & the normal to the surface.
All types of waves may undergo reflection: water waves off of rocky shore, echos of sound waves, light waves off of mirrors or off of objects.
Wave Behavior: Diffraction
                                                            
Diffraction: wave encounters an obstacle in its path:  waves spread out around the edges of the object.
All types of waves may undergo diffraction: water waves spread out behind a slit (if width is = or < wavelength). Sound waves: we can hear around corners.  EM Waves- radio waves spread out around building between radio station transmitting & radio receiving antenna.  Visible light waves undergo diffraction when pass thru small slits called diffraction gradients and spread out illustrating ROYGBIV.
Diffraction Gradients
Diffraction gradients separate colors in a light source. 3 different types of light sources will yield 3 different patterns of colored light.
Wave Behavior: Interference
interference
Interference pattern- a pattern formed by the overlapping of two or more waves that arrive in a region at the same time. Interference is a characteristic of all wave patterns (sound, light, water) and can increase, decrease, or neutralize waves.

Reinforcement

constructive interference- addition of two or more waves when wave crests overlap to produce a resulting wave of increased amplitude

in phase- term applied to two or more waves whose crests (& troughs) arrive at a place at the same time so that their effects reinforce each other

Cancellation

destructive interference- combination of waves where crests of one wave overlap troughs of another, resulting in a wave of decreased amplitude

out of phase- term applied to two waves for wh/ the crest of one wave arrives at a point at the same time that a trough of the second wave arrives. Their effects cancel each other

standing wave- wave in which parts of the wave remain stationary & the wave appears not to be traveling. A standing wave is the result of interference between an incident (original) wave & reflected wave.
nodes- any part of a standing wave that remains stationary
antinodes- the positions on a standing wave where the largest amplitudes occur
When 2 waves of equal amplitude & wavelength pass thru ea. oth. in opp. dir., the waves are always out of phase at the nodes...nodes are stable regions of destructive interference.
Thin Film Interference
 
The colorful patterns that you see when light reflects off a compact disk are produced by thin film interference. The CD is made of a polycarbonate wafer which is coated with a metallic film, usually an aluminum alloy. The aluminum film is then covered by a lacquer coating.
 
 
Wave Behavior: Source of Vibration/ Disturbance is Moving
bug is stationary
bug bobs in water at constant frequency
crests of waves make concentric circles
wavelengths are equal for each wave
waves hit points A & B at same time
............

bobbing bug swims across water
bug bobs in water at constant frequency bug’s speed is less than wave’s speed
center of outer crest made w/ bug in center of that circle
center of next smaller crest made when bug was in center of that circle
centers of circular crests move in direction of swimming bug
pt B encounters waves of higher frequency because each successive crest has shorter distance so they arrive at B more frequently
pt A encounters waves of lower frequency
because each crest has to travel farther than one ahead of it due to motion of the bug

Doppler effect- the change in frequency of a wave due to the motion of the source or of the receiver. Doppler wave- a wave that is the result of the motion of the source

Doppler effect with sound waves

Source of the sound is moving.
Hearing the changing pitch of a car horn or siren as the vehicle passes you.
As vehicle approaches.you...the pitch sounds higher than normal....bcs of a increase frequency
As vehicle passes you....the pitch sounds lower than normal....bcs of a decrease in frequency

"As the police car approaches, the sound waves from its siren are compressed towards the observer. The intervals between waves diminish, which translates into an increase in frequency or pitch. As the ambulance recedes, the sound waves are stretched relative to the observer, causing the siren's pitch to decrease. By the change in pitch of the siren, you can determine if the ambulance is coming nearer or speeding away. If you could measure the rate of change of pitch, you could also estimate the ambulance's speed." from Harvard Physics Department
"The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for the observer and the source are approaching and an apparent downward shift in frequency when the observer and the source is receding. The Doppler effect can be observed to occur with all types of waves - most notably water waves, sound waves, and light waves." from The Physics Classroom
"The Doppler effect is observed because the distance between the source of sound and the observer is changing. If the source and the observer are approaching, then the distance is decreasing and if the source and the observer are receding, then the distance is increasing. The source of sound always emits the same frequency. Therefore, for the same period of time, the same number of waves must fit between the source and the observer. if the distance is large, then the waves can be spread apart; but if the distance is small, the waves must be compressed into the smaller distance. For these reasons, if the source is moving towards the observer, the observer perceives sound waves reaching him or her at a more frequent rate (high pitch); and if the source is moving away from the observer, the observer perceives sound waves reaching him or her at a less frequent rate (low pitch). It is important to note that the effect does not result because of an actual change in the frequency of the source. The source puts out the same frequency; the observer only perceives a different frequency because of the relative motion between them." from the Physics Classroom
"The Doppler effect doesn't just apply to sound. It works with all types of waves, including light. Edwin Hubble used the Doppler effect to determine that the universe is expanding. Hubble found that the light emitted by the galaxies was shifted toward higher frequencies, or the red end of the spectrum. This is know as a red Doppler-shift, or a red-shift. If the galaxies were moving toward Hubble, the light he observed would have been blue-shifted." from Windows To the Universe
police calculate car’s speed by measuring Doppler effect of radar waves
radar waves sent out by radar gun at a constant frequency....hit approaching car...
radar is reflected off car back to radar gun...but car is moving towards radar gun...
therefore wavelength is smaller and frequency is higher...computer in radar gun
compares frequency of radar emitted by antenna w/ freq. of reflected radar wave of car
 

bow wave- a V shape wave produced by an object moving on a liquid surface faster than the wave speed

bow wave appears to be dragging behind the object producing the wave

occurs in water
are 2-dimensional
produced by overlapping circular waves that form a V
bow wave is example of constructive interference....with big increase in amplitude
occurs when speed of source in a medium is as great as the speed of the wave it produces
....the crests pile up or superimpose on one another directly in front of source

speedboat moving through water quickly will produce (many overlapping circular wave crests)....a bow wave ...a V shaped wave

 

shock wave- a cone-shape wave produced by an object moving at supersonic speed through a fluid

The shock wave produced by overlapping spheres that form a cone.The conical shock wave continues to spread out until it hits the ground. Source must be moving faster than speed of sound to get the overlapping spheres that form cone (of compressed air).

sonic boom- the sharp crack heard when the shock wave that sweeps behind a supersonic aircraft reaches the listener
A supersonic object (aircraft) is not source of sound but as it travels at supersonic speeds it produces its own sound as waves of air are generated to sides of moving object.
These waves move out in 3-dimensional pattern behind plane forming a cone of high
pressure continuously behind plane.
When this front of high-pressure air reaches the ground to a listener....they hear sonic boom
sonic boom is a continuous front of high pressure generated by faster-than-sound sources