Chapter 14 Flashcards
How can Energy can be transferred?
By means of particles’ direct contact, such as one object pushing another
or indirect contact, such as throwing a ball.
By waves
Defn: A wave
is a disturbance that transfers energy through matter or space.
→ mechanical waves (e.g. water, sound, spring or rope) require a medium. electromagnetic waves (e.g. light, radio waves, X-rays) do not require a medium.
Things we learned in the demonstrations with the slinky
→ A pulse is a single disturbance, waves are composed of multiple pulses.
→ The particles of the medium move, but do not travel with the wave.
There are three different kinds of waves.
Transverse waves, longitudinal waves, torsional waves
Transverse waves
are waves in which the vibrations are perpendicular to the direction of wave travel. (e.g. light, piano strings, guitar strings)
Longitudinal waves
are waves in which the vibrations are parallel to the direction of wave travel. (e.g. sound) Note: Water waves are often considered to be transverse, but in reality, they include both transverse and longitudinal vibrations.
Torsional waves
are waves in which the medium transfers energy by twisting back and forth. → you don’t need to know anything else about these.)
What are waves caused by?
Waves are caused by the repeated motion of a vibrating source.
Characteristics of Repeated Motion (e.g., a pendulum)
Cycle, Period and Frequency
Cycle
- 1 cycle is one complete repetition.
- One wavelength
Period
- the time for one cycle or Symbol: T ; Units: s
Frequency
- the number of cycles that occur in each second 1 cycle Symbol: f; Units: Hz (c/s) 1 → Frequency and Period are reciprocals of each other: f = 1/T & T = 1/f
If the frequency of the source is increased, where will the crests be?
If the frequency of the source is increased, the crests will be closer together.
A transverse wave 2 main parts:
The high parts are called crests and the low parts are called troughs. (If the motion is sideways, choose one direction to call crests and the other troughs.)
A longitudinal wave 2 main parts:
The parts where the particles are closer together than normal are called compressions and the parts where the particles are further apart than normal are called rarefactions:
®Defi. The wavelength of a wave
is the distance from one crest to the next (or one trough to the next). → For a longitudinal wave, it is the distance from one compression to the next (or one rarefaction to the next.)
Wavelength symbol and units:
Symbol: 入 ; Units: m
To find how fast a wave travels, i.e, the speed of the wave:
we need the distance it travels in a certain amount of time.
v = d/t = 入/T Since f= 1/T
The Universal Wave Equation. =
v = f 入
The amplitude of a wave
is the distance from the rest position to maximum displacement.
i.e., the amplitude is ½ the distance from extreme to extreme
Amplitude Notes:
- The amount of work you do is the amount of energy you transfer, and it takes more work to produce a wave with a large amplitude than to produce one with a small amplitude. This suggests the following important fact:
- The amplitude is the factor that represents the amount of energy transferred by the wave. i.e., the greater the amplitude, the more energy is being transferred.
- The other factors (wavelength, frequency, period, speed) are not representative of the amount of energy.
Can two waves occupy the same space without affecting each other?
Two waves can occupy the same space without affecting each other. However, they do interfere with each other, causing the medium to react to the combination of the two waves.
Wave Behaviour - reflections/ invertion
The speed of a wave depends on the medium. Whenever a wave travels from one medium to another, part of the wave travels on and part is reflected.
→ If the 2nd medium is more dense than the 1st, the reflected wave is inverted.
→ If the 2nd medium is less dense, the reflected wave is not inverted.
Defn. Interference
Occurs when two or more waves act simultaneously on the same particles of the medium.
- The waves themselves are unchanged, only the medium is affected.
- The effect of two waves on the particles of the medium is analyzed using the Principle of Superposition
Constructive Interference
occurs when the two waves have displacements in the same direction. The resultant displacement is greater than that caused by either wave alone.
Destructive Interference
occurs when the two waves have displacements in opposite directions. The resultant displacement is less than that caused by the largest of the component waves.
Standing Waves
A Standing Wave is formed when 2 waves of the same amplitude and wavelength interfere. The resulting pattern remains stationary (i.e., it does not appear to be traveling).
- The amplitude of the standing wave is twice that of the 2 interfering waves.
- Although standing waves were demonstrated with transverse waves, the same ideas apply to longitudinal waves as well.
nodes
- Points that remain at rest at all times
What do we treat our study of waves as?
We treat our study of waves as though they were ideal waves → waves that do not lose amplitude as they travel.
Antinodes
- Points that experience maximum displacement
What must be the length of a medium for a standing wave to occur?
- In a given medium, only certain wavelengths can maintain a standing wave pattern.
→ The length of the medium must be a multiple of half the wavelength.
What occurs where double crests or double troughs occur?
Nodes and antinodes
Principle of Superposition
- The displacement of a medium caused by 2 or more waves is the sum of the displacements caused by the individual waves. gives nothing
Difference between transverse and longitudinal waves:
Transverse waves have crests and troughs; Longitudinal waves have compressions and rarefactions.
In transverse waves, the motion of the particles of the medium is perpendicular to the direction of the wave; In longitudinal waves, the motion of the particles is parallel to the direction of the wave.
Speed in waves:
When a wave travels from one medium to another, the speed changes.
- If speed increases, the wavelength increases, but the frequency does not change.
What doe the frequency of the wave depend on?
The frequency of the wave depends only on the source.
What does the speed of the wave depend on?
The speed of the wave depends only on the medium.
what does the wavelength of the wave depend on?
The wavelength of the wave depends on the frequency of the source and on the medium.
Does the frequency, speed, or wavelength depend on the amplitude?
No
When are transverse waves inverted, when are they not?
Transverse waves reflected from fixed ends are inverted, from free ends are not.
What are waves on a spring called?
Waves on a spring are called 1-dimensional waves. They move in only one dimension. (The energy travels only along a straight line.)
Do 2 dimensional transverse waves have crests and troughs?
Like 1-dimensional transverse waves, they have crests and troughs.
How do waves in water move?
- Waves in water move in two dimensions. (Light waves move in three dimensions.)
A wavefront:
is a continuous crest or trough.
The direction of a 2-d wave
is perpendicular to the wavefront.
In 2 dimensional transverse waves what does frequency and wavelength depend on?
@Frequency depends only on the source, but wavelength and speed depend on the medium.
What do waves with higher frequency have? (2 dimensional)
shorter wavelength.
Do waves move slower in shallower water?
Yes, waves move slower in shallower water (therefore, they have shorter wavelengths).
Speed of waves in 2 Dimensional
Different wavelengths have (virtually) the same speed in a given medium.
Reflection of Waves
Reflection of waves is very important for everyday life example: Sound waves → without reflection we couldn’t hear around corners (e.g. sound from stereo in another room)
→ echoes example: Light waves without reflection we couldn’t see anything (other than things that produce their light) because what we see is reflected light. → mirrors -
Reflection in 1D vs. 2D
1-dimensional waves → reflect from fixed end inverted; from loose end uninverted.
- With 2-dimensional waves, our main concern is the direction of reflected waves.
Using wavefronts:
→ The angles of incidence and reflection are the angles between the wavefronts and the barrier.
— It is easier to analyze reflection of waves using wave rays rather than wavefronts.
wave ray
an arrow showing the direction of wave travel
normal
a line perpendicular to a barrier: 90 degree angle to surface
angle of incidence
the angle between the incident wave ray and the normal
Law of relection
the angle of incidence = angle of reflection
angle of reflection
the angle between the reflected wave ray and the normal
Refraction
bending of waves as they travel from one medium to another at an angle (they do not bend if they cross the boundary straight on.)
Reflection of waves by a parabolic reflector:
straight waves reflect to a focal point
ex. satellite dishes, parabolic microphones
- circular waves generated at the focal point reflect as straight waves ex. flashlights
Why do we have rainbows, telescopes, binoculars, etc.
Refraction
What happens as waves travel into a slower medium at an angle?
they bend toward the normal, and the λ decreases: the angle of incidence is greater than angle of reflection
What happens as waves travel into a faster medium at an angle?
they bend away from the normal, λ increases: the angle of incidence is less than angle of reflection
Diffraction
the bending of waves as they pass by the end of a barrier or go through an opening in a barrier
ex. cities that have breakwater to reflect wave energy away from the shoreline, there is a opening so that boats can go through
WAVE LENGTH DOES NOT CHANGE
what does the amount of diffraction depend on?
the wave length:
longer wavelength are more diffracted than shorter ones
the size of the opening:
smaller opening causes greater diffraction
What is affected in interference of 2 dimensional waves
- only medium is affected
What is used to determine the resulting displacement in interference of 2 dimensional waves?
Pricipal of superposition
When does constructive interference occur in interference of 2-dimensional waves?
where crests meet crests and where trough meets through
When does destructive interference occur in interference of 2-dimensional waves?
where crest meets a trough
What do you get when continuous waves of the same amplitude and frequency meet in interference of 2-dimensional waves?
standing waves which have nodes(points of no motion) and antinodes or loops (sections of maximum displacement)
When two waves with equal frequency and amplitude interfere:
an interference pattern similar to a standing wave pattern results.
Nodal lines are formed…
where destructive interference occurs. (where crests and troughs meet).
Antinodal lines are formed…
where constructive interference occurs. (double crests and double troughs).
Nodal lines and anti-nodal lines are in the shapes of…
hyperbolas.
Higher frequency results…
in more nodal lines which are closer together.
Instead of two-point sources, could a straight wave could be produced?
Instead of two point sources, a straight wave could be produced which then encountered a barrier with two small openings. The diffraction through the openings would result in two circular waves just like those from two point sources.
- With water, the pattern can be produced by either method. However, when producing an interference pattern for light, the second method is always used since it results in two waves perfectly in phase with each other, something which is impossible to produce with two separate light sources
