Periodic motion, waves and sound Flashcards
angular freq, w =
w = √(k/m)
k = stiffness in spring m = mass
simple harmonic motion, F =
Why is it neg?
F = -kx
Neg to show that restoring force is in opposite direction of the displacement
simple harmonic motion, a =
a = w^2x
what is the eq point
point where F = 0.
the point about which the particle or mass oscillates
what is the linear restoring force?
always directed back to eq pt
mag is directly proportional to displacement
what are the 2 types of simple harmonic motion?
Mass-spring
simple pendulum
what is the equation for displacement of a particle from eq pt?
x = Xcos(wt)
X = particle amplitude (largest distance from eq pt) t = time w = 2pif = 2pi/T
Equation for angular freq, w =
w = 2pif
w= 2pi/T
potential E of spring at rest, U =
U = 1/2kx^2
what is the U for a pendulum?
U = mgh where h is height above lowest point
what are the U and K at eq pt?
U = 0
K is max (kinetic E)
in SHM (simple harmonic motion), do f and T depend on amplitude?
no
k = ?
For mass=spring
for simple pendulum
k = spring const
k = mg/L
w =
mass-spring
pendulum
w = √ (k/m)
w = √(g/L)
T =
mass-spring
pendulum
T = 2pi√(m/k)
T = 2pi√(L/g)
f =
mass-spring
pendulum
f = 1/T = w/2pi
f = 1/T = w/2pi
K
mass-spring
pendulum
where is Kmax?
K = 1/2mv^2 Max at x=0
K = 1/2mv^2 Max at a=0
U =
mass-spring
pendulum
Umax?
U = 1/2kx^2 Mat at +/-x
U = mgh Max at a
For SHM where does max acc happen?
always at Fmax. which occurs at max displacement, x
what is a transverse wave?
particles oscillate perpendicular to direction of wave motion.
Think waving a slinky back and forth on the ground
longitudinal waves
oscillate along direction of wave motion
think pushing slinky
wave equation y =
(where y is the displacement of a particle
y = Ysin(kx-wt)
where Y = amplitude
k = wave number
what is wavelength, h
the distance from one max crest to the next
what is f and what are the units
freq is the # of waves passing a pt per second.
Hz
velocity of wave, v =
v = hf
wave number k =
k = 2pi/h
what is phase difference?
what if it is 0?
phase diff is how in step 2 waves are
at 0, they are identical
what is the principle of superposition?
constructive vs. destructive
when waves interact, the result is the sum of the waves
constructive, waves are in phase and amplitudes add
destructive - out of phase, amp is difference
what is a traveling wave?
one side is fixed, the other end is moved from side to side. Think of moving a string side to side, the other part is attached to the wall.
Results in an incident wave, which travels from the open end (your hand), to the wall
Also in a reflected wave, the wave that travels back after hitting the wall.
If you keep moving your hand, there are 2 waves moving at once then.
what is a standing wave?
what are the parts?
Besides strings, where can standing waves occur?
wave form that has 2 fixed ends. So it remains stationary, but the amplitude fluctuates.
Like a jump rope, only imagine you’re not moving your arms.
node - pt that remain at rest
antinode - halfway between nodes, amplitude changes. (max, min, max, min)
standing waves occur in strings, also in pipes, closed
resonance:
natural freq
mass-spring?
pendulum?
the natural freq is the normal mode of vibration, no external forces.
mass spring will have infinite natural:
f = 1/2pi[√k/m
pendulum as 1 natural freq:
f = 1/2pi√g/L
what is forced oscillation?
is the amp usually large or small?
forced oscillation is when a periodically varying force is applied to a systme.
amp usually small
larger is F is close to natural freq
what does it mean if the system is resonating?
forced oscillation F = nat freq.
amp is at max, if system was frictionless, forced oscillation would continuously add to system and amp would get infinitely large
sound waves are what kind of waves?
longitudinal
What are the 3 classifications of sound waves?
infrasonic = 20,000 Hz
what is intensity of sound?
P =
rate at which E is transported across perp surface by wave
P = IA
where P is power
I = intensity
A is area
how is sound level measured
B = 10logI/Io
where Io = reference intensity
can pitch be measured?
no
How can sound be produced?
solid?
vibration?
vibration of solids, air mcules put in motion, eg string instrument, piano (moving parts)
acoustic viibration - organ pipes, flute, no moving parts just air vibrating
what are beats?
beats are heard when 2 waves of nearly the same freq are superimposed. The waves are added together, leading to a periodic variation of loudness. = beats!
freq of beats = |diff in indiv freq|
Doppler effect
perceived f is different than real:
f’ = f [(v+/-vD)/(v+/-vS)]
doppler effect, eq when detector is moving toward source of source moves toward detector
vD is + Think the source and detector are moving closer to each other, so the detector is getting close to detection
when detector moves away or source moves away
vD is - Think the detector is getting further away from detection
Standing waves: wavelength, “h” and f
strings
string:
h = 2L/n where n is harmonic
f = nv/2L where v = wave speed
standing waves, h and f for
open pipes
closed pipes
open:
h=2L/n
f = nv/2L
closed:
h = 4L/n
f = nv/4L
higher harmonics have longer or short h?
they have shorter.
Think how many “waves” can you get in fixed position? higher harmonics mean you can get more, 3rd harmonic, you can fit 3 full waves in the fixed space, so lengths are shorter
