Chapter 5 - Periodic Motion and Waves Flashcards
Equation: wavelength (first harmonic)
λ1 = 2L/1
Equation: frequency of standing waves
fn = nv/2L
n = # harmonic
Equation: frequency of standing waves in relation to the fundamental frequency
fn = nf1
What is a standing wave?
It appears to have no propagation velocity and is the result of the interference of two waves traveling in opposite directions
Does waves transfer matter or energy?
just energy
Equation: wavelength (second harmonic)
λ2 = 2L/2
What two forces act on a simple pendulum?
weight (mg) and tension (perpendicular to the arc)
What is the frequency of a wave?
the number of vibrations of the wave per unit time
What is simple harmonic motion?
vibrating motion, as an object moves back and forth
Equation: restoring force of pendulum
Frestoring = -mgsinθ
What is meant by an object said to be elastic?
The object experiences a deformation while being compressed or stretched.
Equation: frequency of a spring system
f = 1/2π √(k/m)
Equation: frequency of a pendulum
f = 1/2π √(g/L)
Define amplitude of motion (A)
the magnitude of displacement of the object from equilibrium
Equation: wave velocity in regards to frequency
v = λf
Equation: frequency of first harmonic (fundamental frequency)
f1 = v/2L
In a standing wave, what are nodes
areas of no vibration
What is the amplitude of a wave?
magnitude of maximum displacement of a wave from its point of equilibium
Diagram of standing wave: first harmonic
If a spring is let go, where is kinetic energy the smallest (0)?
at the greatest magnitude of amplitude (greatest compression and greatest stretch)
What is a beat?
when two waves of differing wavelengths interfere with each other
What is meant by the negative sign in Hooke’s Law?
The spring experiences a restoring force that acts in the opposite direction of the spring’s displacement.
Equation: wavelength (third harmonic)
λ3 = 2L/3
What is the principle of superposition? When does it not hold?
It two or more waves passing through the same medium meet at a particular point in that medium, the net displacement by those waves is the addition of the individual displacements by the waves as if they were traveling through the medium alone. The only time it does not hold is when the waves’ amplitudes are large enough that combined, they change physical properties of the surrounding medium.
Define period of motion (T)
the time required to complete one full cycle of motion (time/vibration)
What is dampened harmonic oscillation?
The system loses energy as it vibrates, but retains a constant period (because amplitude and speed both decrease).
Equation: potential energy of a spring
Uspring = 1/2kx2
If a spring is let go, where is kinetic energy the greatest?
at the line of equilibrium
What are the units of the spring constant?
N/m
If you let a pendulum go, where is the kinetic energy the smallest (0)?
at the greatest magnitude of amplitude
Describe transverse waves
They cause vibrations perpendicular to the direction of wave propagation
Equation: period of first harmonic
T1 = 2L/v
If you let a pendulum go, where is the kinetic energy the greatest?
at the bottom of the arc, equilibrium (the nadir of the path)
Equation: potential energy of a pendulum
Upendulum = -mgL (1-cosθ)
What is wavelength of a wave (λ)?
the distance between two identical points (crest-crest or trough-trough) of disturbance in a wave
Equation: frequency in terms of period
f = 1/T
Diagram of standing wave: second harmonic
What is the speed of a wave?
how far the wave travels per unit time
In a standing wave, what are antinodes?
the areas of greatest amplitude (between nodes)
What is destructive wave interference?
superposition of two waves that are out of phase
If they are of equal amplitude, they will lead to no amplitude, but continue as normal after they have passed each other.
Equation: Average force needed to compress a spring
-kx/2
Equation: Hooke’s Law of force needed to a displace a spring
F = -kx
What is resonance?
amplitude/energy of a system may increase if there is a supplied vibrating force that has a frequency which is the same as the natural frequency of the system (pushing a swing at the right time, a singer shattering a glass, NMR)
Equation: period of a pendulum
T = 2π √(L/g)
Equation: wavelength of standing waves
λn = 2L/n
n = # harmonic
Define frequency of motion (f or ν)
the number of vibrations that occur during a specified amount of time (Hz, vibrations/second)
Describe longitudinal waves
They cause vibrations parallel to the direction of wave propagation.
Equation: beat frequency
fbeat = l f2-f1 l
Equation: period of a spring system
T = 2π √(m/k)
Which type of standing wave has the longest possible wavelength?
first harmonic
What is constructive wave interference?
superposition of waves that are in-phase
If they are of equal wavelength, they will create an amplitude twice as high, but continue as normal after they have passed each other.
Equation: transverse wave velocity along a string
v = √(T/μ)
T = tension in string
μ = mass per unit length
Equation: wave velocity in regards to period
v = λ/T
