Chapter 9: Periodic Motion, Waves, and Sound Flashcards
Simple Harmonic Motion is:
Repetitive motion of an oscillating system in which a particle or mass oscillates about an equilibrium position and is subject to a linear restoring force.
Equation to determine the restoring force of a spring (Hooke’s Law):
F = -kx
where k is the spring constant and x is the displacement of the spring from its equilibrium length
The higher the k value of a spring, the more:
stiff the spring is, and the greater the magnitude of restoring force for any given displacement
Equation to determine the acceleration of a spring:
a = -ω2x
where ω is the angular frequency and is equal to 2πf and rad(k/m)
Equation to determine the angular frequency (ω) of a spring:
ω = 2πf = √(k/m)
where m is the mass of the object
Frequency is a measure of:
the rate at which cycles of oscillation are being completed.
SI unit of frequency:
hertz (Hz)
SI unit of anglular frequency:
r/s (radians per second)
One radian is equal to:
180/π
so 2π radians is equal to 360 degrees (a full circle)
Two springs with identical k and m values but that are stretched at different lengths will always experience the same:
frequency of oscillation
Frequency describes:
the number of oscillations per second
A period describes:
how many seconds it takes for one oscillation to occur
A period is equal to:
1/f
where f is the frequency
Equation to determine the potential energy of a spring:
PE = 1/2kx2
Equation to determine the kinetic energy of a spring:
KE = 1/2mv2
A spring’s maximum velocity is at:
the equilibrium point (as it passes through it)
Equation to determine the restoring force of a pendulum:
F = -mgsinØ
where Ø is the angle between the pendulum arm and the vertical
Equation to determine the angular frequency (ω) of a pendulum:
ω = 2πf = √(g/L)
where L is the length of the pendulum
The two factors that contribute to the angular frequency of a spring:
the spring constant and the mass of the object
The two factors that contribute to the angular frequency of a pendulum:
gravity and the length of the pendulum
Equation to determine the potential energy of a pendulum:
PE = mgh
Equation to determine the kinetic energy of a pendulum:
KE = 1/2mv2
Equation to determine the period (T) of a spring:
T= 2π√(m/k)
Equation to determine the period (T) of a pendulum:
T = 2π√(L/g)
Equation to determine the frequency (f) of a spring:
f = 1/T or ω/2π
Equation to determine the frequency (f) of a pendulum:
f = 1/T or ω/2π
At maximum displacement, springs experience:
maximum restoring force, maximum acceleration, maximum potential energy, and minimum kinetic energy
At minimum displacement, springs experience:
minimum restoring force, minimum accleration, minimum potential energy, and maximum kinetic energy
At maximum angular displacement, pendulums experience:
maximum restoring force, maximum acceleration, maximum potential energy, and minimum kinetic energy
At minimum angular displacement, pendulums experience:
minimum restoring force, minimum accleration, minimum potential energy, and maximum kinetic energy
Two types of sinusoidal waves:
transverse and longitudinal
Transverse waves are waves in which:
the direction of particle oscillation is perpendicular to the movement (propagation) of the wave (i.e. water and electromagnetic waves)
In any wave form, energy is delivered in the direction of:
wave travel
Longitudinal waves are waves in which:
the direction of particle oscillation is along the direction of wave propagation (i.e. sound waves)
The frequency of a wave is equal to:
the number of wavelengths passing through a fixed point per second
Wavelength and frequency are:
inverse to one another; having a large wavelength will result in a small frequency and having a short wavelength will result in a high frequency
Equation to determine the speed (f) of a wave =
v = fλ = ω/k = λ/T
Equation to determine the wavenumber (k) of a wave:
k = 2π/λ
Equation to determine the angular frequency (ω) of a wave:
ω = 2πf = 2π/T
Phase difference describes:
how “in step” or “out of step” two waves are with each other.
Two waves are in phase when:
they have the same frequency, wavelength, and amplitude and pass through the same space at the same time (their troughs and crests are in the exact same positions)
When two waves are perfectly in phase, the phase differnce is:
zero
When the trough of one wave is exactly opposite the crest of another wave, the phase difference is:
one-half of a wave, or 180 degrees
Interference describes:
waves meeting in space
Constructive interference describes:
waves meeting in space IN phase; the resultant wave is the sum of the two waves and has a greater amplitude
Destructive interference describes:
waves meeting in space OUT of phase; the resultant wave is the difference of the two waves and has a reduced amplitude
When two waves are exactly 180 degrees out of phase, the resultant wave:
has zero amplitude; the cancel each other out and there is no wave
A traveling wave is:
a wave that can be seen to be moving
When a traveling wave reaches a fixed boundary:
it is reflected and inverted
A standing wave is:
a wave that appears to have a stationary waveform
Nodes are:
points in the wave that remain at rest (don’t move)
Antinodes are:
points in the wave that are midway between nodes; they are the points that fluctuate the maximum amplitude
Natural frequency is:
the frequency or frequencies at which an object will vibrate when disturbed.
Timbre is:
the quality of sound; it Is determined by the natural frequency or frequencies of the object.
Pure tone:
a single frequency
Rich tone:
multiple natural frequencies that are related to one another by whole number ratios
Forced oscillation:
when a periodically varying force is applied to a system, and the system is driven at a frequency equal to the frequency of the force
When the frequency of a applied force is close to that of the natural frequency of a system, the amplitude of oscillation:
becomes larger
If the frequency of a periodic force is equal to a natural frequency of a system, the system is:
resonating (the amplitude of oscillation is at a maximum)
Sound is:
a longitudinal wave of oscillating mechanical disturbances of a material
Sound can travel through solids, liquids, and gases, but not:
a vacuum.
Sound travels fastest through:
a solid
Sound travels slowest through:
a liquid
Audible wave frequency:
20 Hz to 20,000 Hz
Infrasonic wave frequency:
< 20 Hz
Ultrasonic wave frequency:
> 20,000 Hz
Sound is produced by:
the mechanical disturbance of the particles of a material, creating oscillations of particle density that are along the direction of movement of the sound wave
Equation to determine the intensity of a wave:
I = P/A
where P is the power and A is the surface area of the object the wave comes in contact with
SI units of intensity:
W/m2
Intensity of a wave is proportional to:
the square of the amplitude of the wave
(I = Amplitude2)
Intensity of a wave is inversely proportional to:
the square of the distance the wave traveled from the source
Equation to determine the sound level (B):
B = 10log(I/Io)
where Io is 1 X 10-12 (the threshold of hearing)
Equation to determine the new sound level after the intensity of a sound is changed by some factor:
Bf = Bi + 10log(If/Ii)
where (If/Ii) is the ratio of the final intensity to the initial intensity
Loudness of sound is related to the sound’s:
intensity (which is proportional to the sound’s amplitude squared
Pitch of a sound is related to the sound’s:
frequency
Equation to determine the beat frequency:
fbeat = |f1 - f2|
The Doppler Effect is:
A shift in the perceived frequency of a sound compared to the actual frequency of the emitted sound when the source of the sound and its detector are moving relative to each other
In the Doppler Effect, the apparent frequency is higher when:
the source of a sound and its detector are moving toward each other
In the Doppler Effect, the apparent frequency is lower when:
the source of a sound and its detector are moving away from each other
Equation to determine the perceived frequency from the Doppler Effect:
when the source and detector are moving towards each other, use the top signs. When they are moving away from each other, use the bottom signs.
Standing waves are produced by:
the constructive and destructive interference of two waves of the same frequency traveling in opposite directions in the same space.
The points in a standing wave with no amplitude fluctuation are called:
nodes
The points in a standing wave with maximum fluctuation are called:
antinodes
Equation to determine the wavelength of standing waves for strings and open pipes:
λ = 2L/n
where L is the length of the string or pipe and n is the number of antinodes.
Equation to determine the frequency of a standing wave for strings and open pipes:
f = nv/2L
where n is the number of nodes and L is the length of the string or pipe.
The closed end of a pipe or string supports a:
node
The open end of a pipe or string supports a:
antinode
Equation to determine the wavelength of standing waves for closed pipes:
λ = 4L/n
where L is the length of the closed pipe and n is the number of nodes
Equation to determine the frequency of a standing wave for closed pipes:
f = nv/4L
where n is the number of nodes and L is the length of the closed pipe
