Oscillations Flashcards
Period
symbol: T
duration of one cycle in a repeating event
unit: s
Frequency
numbers of cycles per unit time - the reciprocal of period
f = 1/T
Unit: Hz
Angular frequency
The scalar absolute value of angular velocity.
ω= 2pi*f
Point of equillibrium
point around which the system oscillates, and the force acting on the object is zero
V = max a = 0 A = 0
Displacement
symbol: y
the momentary distance of the oscillating object from the point of equilibrium
Amplitude
point of maximal displacement
Harmonic oscillation
oscillation along a straight line, in which the displacement is a sine function of time
y= Asin(ωt+ φ)
Velocity of object in harmonic oscillation
v = ωAcos(ω*t+ φ)
Acceleration of object in harmonic oscillation
a = ω^2Asin(ω*t+ φ)
Maximal velocity of object in harmonic oscillation
v = A*ω
Maximal acceleration of object in harmonic oscillation
a = ω^2*A
Force acting on an object in harmonic oscillation
Force acting on an object in harmonic oscillation is proportional to displacement. The force always points at the point of equilibrium, this is why it’s called restoring force.
F= -mω^2y
Oscillator
a physical system capable of oscillation
Mass-on-spring/ Pendulums
Acts as simple harmonic oscillators if there is no loss of energy during their motion
Natural frequency of an oscillator
f = 1/2π*sqr(k/M)
wha mass is displaced from its equilibrium position and released, the elastic spring force of the spring will cause the system to undergo simple harmonic oscillation spontaneously, providing negligible energy loss. A spontaneous oscillation like this proceeds on its own without external influence, it is called free oscillation an it has a natural frequency, calculated from the formula above.
Damped oscillation
oscillation subjected to energy loss and decrease of it’s amplitude. In every real system, there is some kind of damped oscillation. The amount of damping is dependent the internal structure of the system and on its interactions with the environment.
E.g: Push swing and leave
Driven oscillation
an external periodic force acts on the system besides the restoring force.
E.g: Mother keeps swinging
Resonance
Vibration together. Systems meets and influences each others oscillations. Strong damping lowers natural frequency and weak damping increases it. High driving force increases amplitude until natural frequency, then decreases.
Damping is caused by togetherness of systems.
Resonance catastrophe
Bridge
Wave
Propagation of oscillation in a medium. Has temporal and spatial periodicity (time and space).
Wavelength
distance between points of a wave that has the same phase
unit: meter
Velocity of propagation
c=f*lamda
the velocity of the points in a wave that are in the same phase
this wave relationship applies to all kinds of waves
What is an internal property of a wave?
Frequency. It remains constant even when the wave passes from one medium to another.
Velocity of propagation and wavelength depends on the properties of the medium they are traveling in.
Transverse waves
the direction of oscillation is perpendicular to the direction of propagation . the direction of oscillation may vary while it always remains perpendicular.
e.g: surface waves in water and electromagnetic waves (light)
Does not specify plane
Longitudinal wave
the direction of oscillation is parallel to the direction of propagation.
sound waves can act as transverse and longitudinal. they can be longitudinal and transverse in gases and liquids, but only transverse in solids.
Linear polarization
One direction of propagation is selected from a transverse wave to linearly polarize it. In a linearly polarized wave the plane of oscillation and the direction of propagation remains constant with time.
Light can be polarized (sunglasses).
Wavefront:
the surface containing points of waves in identical phases
Spherical waves
waves originating from a common point but propagating in every direction in space. Wavefronts are concentric spherical surfaces
2D: Circular wave in a pond
Plane waves
all the wavefronts are parallel to each other but perpendicular to the direction of propagation
2D: Rope
Reflection
incident wave turning back at the interface between different media
angle of incidence is equal to the angle of reflection
angles are measured in relation to the normal axis. normal axis and the lines of propagation are in the same plane
How is the color of objects determined?
By the reflecting properties (in case of opaque materials)
Refraction
the change of direction of propagation of a wave when passing through an interface between two media. the relationship of the angles are before and after passing through the media
Law of refraction/Snells law
sinalpha/sinbeta=ci/c2
Interference
Occurs when two or more waves meet. The meeting waves has identical wavelengths and their phase differences are constant in time
Constructive interference
when two waves superpose in identical phases
if two waves have equal amplitude and identical phases, the resultant amplitude will be twice the size
Destructive interference
when two waves superpose in precisely opposite phases, the waves becomes smaller
Partial construction or deconstruction
When phases are just a little bit different from each other
Standing waves
Resultant pattern of interference between plane waves that propagate against each other and have identical wavelengths and amplitudes. The resultant waves will appear as standing in stead of propagating. Each point in a standing wave oscillate with different amplitudes. Amplitudes are zero in nodes and maximal in the middle of two nodes.
l=k*(lambda/2)
If l is shorter, lambda is shorter as well
Diffraction
Can be a result of interference.
Change in the direction of a wave propagating due to an obstacle or slit in the path of a wave.
If the slize of the obstacle or slit is greater than the wavelength, there will be no change in direction. The smaller the size of the slit, the greater the effect of diffraction.
Huygens-Fresnel principle
According to this model, every point on a wavefront acts as a source of new elementary waves. These points cannot be seen, but can be imagined as spherical waves propagating in every direction in space.
If the slit is only a point only one spherical wave will originate from this point, and there will be only one new wavefront since there are no elementary waves to interfere with. The diffraction will be total.
Sound
mechanical vibration that propagates as a wave in compressible materials.
Infrasound
less than 20 Hz
Ultrasound
20 000 - 10^5 Hz
Audible sound
20 - 20 000
Hypersound
10^9
Sounds propagating in gases and liquids
As longitudinal waves. Density and pressure fluctuations may occurring in the mediums.
Pitch of sound
Determined by frequency,
Loudness of sound
Determined by amplitude
Speed of sound
Depends on properties of the medium - > the compressibility
The easier it is to compress a material, the farther are its component molecules from each other and the longer time is required for the molecules to pass on the vibration.
The speed of sound also depends on temperature (less in solids) and pressure (especially in gases).
It is independent on frequency
(PP) Which statement is true about the restoring force acting on a harmonically oscillating body?
A) It is directly proportional to the displacement but points to the opposite direction
B) It is inversely proportional to the displacement but points to the opposite direction
C) It is directly proportional to the displacement and points to the same direction
D) It is inversely proportional to the displacement and points to the same direction
C
(PP) An object is oscillating with 5 Hz frequency. Which statement is true?
A) The object oscillates once in 5 seconds
B) The object oscillates 5 times in one second
C)The amplitude of the oscillation is 5 cm
D) The oscillation of the object terminates after 5 swings
B, because T=0,2
(PP)Which one is the frequency range of audible sounds for human hearing? A) <20 Hz B) 20 - 20 000 Hz C) 20 000 - 10^5 Hz D) 10^9 Hz
B
(PP)Which statement is true about polarization?
A) When two polarizers are oriented parallel, light cannot pass through them.
B) The polarizer selects precisely two planes from polarized light
C) The majority of common light sources emit polarized light
D) Longitudinal waves cannot be polarized
A
(PP)What phenomenon can we observe if a wave passes through the slit with a width that is ten times wider than the wavelength? A) Diffraction B) Refraction C) Reflection D) Absorption
D
(PP)The frequency of a longitudinal wave is f= 0,25 Hz and its speed of propagation in the given medium is 25 m/s. What is the wavelength? A) 0,01 m B) 6,25 m C) 100 m D) 625 m
C
(PP) What is the wavelength of a 10 kHz sound wave in air? A) 33 mm B) 3,03 cm C) 330 dm D) 30,3 m
A
(PP) It takes 0,4 for a pendulum to move from one side to the other. What is the eigenfrequency?
A) 0,4s
B) 5 Hz
C) 1250 mHz
D) 0,8s
B ??
(PP) In case of a damped oscillation…
A) The amplitude of the oscillation decreases over time but it’s frequency does not
B) Neither the frequency nor the amplitude of the oscillation decreases over time
C) The frequency of the oscillation decreases over time but its amplitude does not
D) Both the frequency and the amplitude of the oscillation decreases over time.
A
(PP) Sound may be a longitudinal wave …
A) In any state of matter
B) Only in liquids and gases
C) Only in liquids
D) Only in gases
B
(PP) An engine makes 2100 revolutions in one minute. Calculate the frequency.
A) 0,0286 Hz
B) 35 Hz
C) 219,9 Hz
D) 2100 Hz
A ??
(PP) It takes 0,4 seconds for a pendulum to move from one side to the other. What is the amplitude?
A) 1,25 Hz
B) 0,4 s
C) Not enough data
D) 0,8 s
C
We know the angular velocity of a rotating object, but nothing else. Which of the following quantities can be calculated in such a case?
A) Tangential velocity and time period
B) None of the options
C) Frequency and time period
D) The frequency and the tangential velocity
C
(PP) A centrifuge makes 10000 revolutions per minute. Its radius is 14 cm, calculate the angular velocity. A) 166,7 Hz B) 0,006 s C) 1047 rad/s D) 10^-4 min
C
It must be C, because it is the only option with correct unit
