simple harmonic motion Flashcards
pressure
force / area Pascals
increasing force = larger pressure
increasing area = smaller pressure
compression
more pressure
peak above x axis
rarefraction
less pressure
peak below x axis
less molecules than atmospheric pressure w/ no sound
wave
a disturbance within a medium that propagates w/ a velocity that depends on the medium
longitudinal wave
energy is transported through the medium w/out permanently transporting matter
sound
medium
any material that has:
mass - therefore inertia
stiffness - therefore restoring forces
a material that has these 2 can vibrate
simple harmonic motion
simplest form of vibratory motion
what does shm require
2 properties of objects
mass
stiffness
spring-mass system
spring mass at rest = equilibrium
w/ external force = spring extended
after removing external source = spring compressed
restoring force pulled it back beyond equilibrium –> makes it continue oscillating
hooke’s law
the restoring force is proportional to the displacement
when this condition is satisfied, the object undergoes SHM
quantifying shm
described by a periodic fucntion sine
more complex motions or signals can be represented as a sum of many sine waves - fourier analysis
visual representation of shm
x axis = distance or time
y axis = displacement, amplitude, or pressure
parameters of shm
amplitude - how big
frequency - how fast
inverse of period - how long
phase - when (where in the cycle)
amplitude
measure of magnitude of the oscillation
period
time taken to complete one full cycle of motion
measured in units of time
frequency
rate of oscillation
how fast the wave repeats
Hz = number of cycles / second
frequency & period
relationship is reciprocal
f = 1/T
if period is halved, what happens to frequency?
frequency is doubled
wavelength
length of 1 cycle of a wave
measured in units of length
higher frequency = smaller wavelength
phase
where you start
0 degrees
90 degrees
180 degrees
270 degrees
formula for shm
x(t) = A sin (2 [pi] f t + [phase])
f = 1/T
shm as uniform vibratory motion
vibratory motion = dot moving around circumference of a circle at a constant rate
if f = 1 Hz, dot goes around circle once / second
sound is shm
happens when a source acts on a medium w/ mass & stiffness
