Princeton Ch 11 - Oscillation and Waves Flashcards
Periodic/harmonic motion.
Any motion that regularly repeats is referred to as periodic or harmonic motion.
Period (T).
The time it takes an object to move through one full cycle of motion. The final position and velocity is equal to the initial values.
For waves,
Frequency.
The number of cycles that occur in one second. [cyclces/second] or [Hz]
For waves, this is how much a wave moves up and down.
Relate period and frequency.
f = 1/T; T = 1/f
Period and frequency are recipricols.
The back and forth motion for a simple block spring attached to the wall can dontinue indefinitely, if the following criteria is met.
If the friction is negligible.
Equilibrium position.
The point at which the net force on the block/object is zero, when the spring is at its natural length. We say x = 0 here.
Simple harmonic motion.
The “ideal” type of oscilatory motion is referred to as SHM. Any motion that regularly repeats is oscilatory.
Hooke’s law.
F = -kx.
k = spring constant x = length of extension or compression
The force required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring.
Why isthe equation for Hooke’s law negative?
F = -kx
The direction of the spring force is always directed opp. to its dispalcement from eq. Compressed springs want to move right, so the direction is positive. Stretched springs want to pull back left; we indicate the direction is left by giving the equation a negative.
Elastic potential energy.
1/2kx²
When we pull a spring to get oscillations, we’re exerting a force over a distance; hence we’re doing work.
We can look at motion of a block attached to a spring from the point of view of back and forth transfer of elastic potential energy and kinetic energy. Explain how.
When the spring is strethced, the block isn’t moving, so all the E is in the form of elastic PE. This PE turns into KE, until x = 0. As the block passes equilibiru, the KE graduatlly turns back into PE until the spring is at max compression, where it’s all transformed back to PE.
Amplitude.
The maximum displacement of the block from the equilibrium, denoted by A.
The KE of a block is at max when x = ?
The KE of a block is at max when x = 0.
The speed of a bloack is at max when x =?
The speed of a block is at max when x = 0.
ΔW(by spring) = ?
ΔW(by spring) = -ΔPE(elastic)
v max of a spring =?
A√k/m
ΔW(against spring) = ?
ΔW(against spring) = ΔPE(elastic)
True or false. To use W = Fdcos(theta), the force has to be constant.
True.
Crest and troughs.
Crest is the peak of a wave. Trough is the bottomost point.
Wavelength.
The distance from one crest to the next (ie the length of one cycle of the wave) is called the wavelength.
True or false. The speed of the wave depends on frequency.
FALSE. The speed of the wave depends on the type of wave and the characteristics of the medium, not the frequency. We can wiggle the end at any frequency we want, and the speed created with be constant. Since v = λf, a higher f must mean a shorter λ.
Wave equation for speed.
v = λf
The speed of a wave is determined by the type of wave and the characteristics of the medium, not by the frequency. What is the one exception to this rule?
Dispersion, discussed in optics is an exception.
When a wave passes into another medium, its speed changes, and its frequency ___.
When a wave passes into another medium, its speed changes, but its frequency does NOT change.
What are two big rules when it comes to waves.
1) The speed of a wave is determined by the type of wave and the characteristics of the medium, NOT by the frequency. This applies to different waves in one medium.
2) When a wave passes into another medium, the speed changes, but its frequency does NOT. This applies to a single wave in different media.
Constructive versus destructive interference.
If crest meets crest and trough meets trough, waves are in phase, and their amplitudes will add; we say these waves interfere constructively.
Another way to say in or out of phase.
In phase: 0°, 360°, 2π
Out of phase: 180 or π radians
If the path difference = __, the waves will be in phase and will constructively interfere.
If the path difference = __, the waves will be 180 out of phase and will destructively interfere.
If the path difference = nλ (n = 1,2,3) the waves will be in phase and will constructively interfere.
If the path difference = (n+1/2)λ, the waves will be 180 out of phase and will destructively interfere.
Standing waves.
The combination of waves traveling left and right, where the horizontal positions of the crests and troughs remain fixed. Points that don’t vibrate up and down will be called nodes. Halfway b/t two consecutive nodes are points where the amplitude is maximized; these positions are called antinodes.
The distance between any two consecutive nodes is always ___.
One-half of the wavelength.
Nodes.
Points that don’t vibrate up and down are nodes. This is where destructive interference occurs.
Standing wave- wavelengths for two fixed ends. λ =?
λ = 2L/n, where n = 1, 2, 3
n is simply the harmonic number. The first harmonic is the fundamental harmonic.
L is the rope length.
Standing wave Frequencies for two fixed ends.
f = nv/2L
Harmonic wavelengths.
λ(n) = λ1/n; λ1 = 2L/1
Harmonic frequencies.
f(n) = nf(1)
