The Nature of Sound II Flashcards
trig and the unit circle
If r = 1 then
cos=x and sin=y
so (x,y) = (cos,sin)
what are rectangular coordinates on the unit circle?
(1,0)
(0,1)
(-1,0)
(0,-1)
what are polar coordinates on the unit circle?
(r,θ)
unit circle quadrants and location
I, II, III, IV
I= top right
II- top left
III- bottom left
IV= bottom right
Uniform circular motion (UCM)
motion of an object in a circular fashion that travels at a constant speed
what is often shown as UCM?
SHM simple harmonic motion
Trace Uniform projected motion
t= 1 unit
sound is created by
movement of air particles and that movement creates pressure variations above and below atmospheric pressure
pressure
reported in Pascals (Pa)
atmospheric pressure values
kilopascals (kPa)
low level sound pressure values
micropascals (µPa)
pressure representations in graphs
- the darker bands overlap with the waveform when it is at its positive peak (more pressure)
- the lighter bands overlap with the waveform when it is at its negative peak (less pressure)
what do the simple signals repeating at a specific rate imply?
- there is a specified # of complete cycles occurring in 1 second
- there is a specific # of seconds or µseconds that elapse when 1 cycle is completed
Wavelength (λ)
distance between two points in a waveform that are the same in terms of pressure
how is wavelength determined?
number of complete cycles in a unit of time and the medium in which the sound pressure variations propagate
wavelength equation
λ= c x T or λ= c/f
c= speed of sound (343 m/s) and t= period
T=1/f
the higher the amplitude…
the higher the energy present in the waveform
5 different ways to describe amplitude
peak amplitude
peak-to-peak amplitude
instantaneous amplitude
RMS amplitude
dB
peak amplitude
max deviation from zero
peak-to-peak amplitude
change between peak (highest amp) and trough (lowest amp)
RMS amplitude
root mean square or average amplitude
PURE TONE= 45 degrees or 0.707 peak
phase
- description of the position of a point in time on a waveform
- relative displacement of waves that have the same frequency
how many degrees is a complete cycle?
360
phase of a sine wave
One complete cycle from 1 to 2
- starting phase is 0 deg
- at the peak the phase is 90 deg
- back at equilibrium the phase is 180 deg
- another quarter cycle the phase is 270 deg
- back at equilibrium is 360 deg or returns to 0
out of phase quarter cycle
if one wave (B) starts before another wave (A), we say that A is 90 deg out of phase with B or that B is -90 deg out of phase with A
- this is because B starts earlier than A
out of phase half cycle
if one wave (C) starts after another wave (A), we say that A is -180 deg out of phase with C or that C is 180 deg out of phase with A
- this is because A starts earlier than
out of phase three-quarter cycle
if one wave (B) starts before another wave (C), we say that B is 90 deg out of phase with C or that C is -90 deg out of phase with B
- this is because B starts earlier than C
phase differences positive
If the phase difference between two waveforms of the same frequency is positive, we say that one wave LEADS the other
phase differences negative
If the phase difference between two waveforms of the same frequency is negative, we say that one wave LAGS the other
phase differences in an in phase sinusoidal
are the same shape and frequency the max and min points occur at the same time
phase differences in an out of phase sinusoidal
are the same shape and frequency the max and min points for each waveforms occur at the different times
when waveform A reaches its maximum value before waveform B reaches its maximum then ….
A leads B
- A reaches its 0 value and its minimum value first
Phase lead
if one waveform reaches its max value before another waveform reaches its max value
Phase lag
if one waveform reaches its max value after another waveform reaches its max value
A & B
- in phase
amplitude doesn’t matter if peak and trough are same (both are sine waves)
A & C
- C leads A (900 ) & A lags C
A is at peak when C is at 0 descending (C is a cosine wave)
A & D
- A leads D (90 deg) & D lags A
A is at peak when D is at 0 ascending (d is a -cosine wave)
B & C
- C leads B (90 deg) & B lags C
B is at peak when C is at 0 descending
B & D
- B leads D (90 deg) & D lags B
B is at peak when D is at 0 ascending
C & D
- C leads D & D lags C
Inverse
C is at peak when D is at trough and they cross at 0 (C= cosine(x) & D= - cosine(x))
REMEMBER PHASE SHIFT DOES NOT CHANGE FREQUENCY, IT JUST MEANS…
TWO SIGNALS ARE AT DIFFERENT POINTS OF THEIR CYCLE AT A GIVEN TIME
