Periodic motion, waves and sound Flashcards by brianne Poynton

angular freq, w =

w = √(k/m)

k = stiffness in spring
m = mass

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simple harmonic motion, F =

Why is it neg?

F = -kx

Neg to show that restoring force is in opposite direction of the displacement

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simple harmonic motion, a =

a = w^2x

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what is the eq point

point where F = 0.

the point about which the particle or mass oscillates

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what is the linear restoring force?

always directed back to eq pt

mag is directly proportional to displacement

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what are the 2 types of simple harmonic motion?

Mass-spring

simple pendulum

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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

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Equation for angular freq, w =

w = 2pif

w= 2pi/T

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potential E of spring at rest, U =

U = 1/2kx^2

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what is the U for a pendulum?

U = mgh where h is height above lowest point

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what are the U and K at eq pt?

U = 0

K is max (kinetic E)

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in SHM (simple harmonic motion), do f and T depend on amplitude?

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k = ?

For mass=spring

for simple pendulum

k = spring const

k = mg/L

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w =

mass-spring
pendulum

w = √ (k/m)

w = √(g/L)

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T =

mass-spring
pendulum

T = 2pi√(m/k)

T = 2pi√(L/g)

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f =

mass-spring
pendulum

f = 1/T = w/2pi

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mass-spring
pendulum

where is Kmax?

K = 1/2mv^2 Max at x=0

K = 1/2mv^2 Max at a=0

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U =

mass-spring
pendulum

Umax?

U = 1/2kx^2 Mat at +/-x

U = mgh Max at a

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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.

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?

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