CSD 202 Exam 1
does 0 dB mean no sound?
NO simply means that the ratio is 1, which is obtained when: Ix=Iref px=pref
external force
Newtonian force (F)- required to move a mass because objects tend to resist any new motion (inertia) F= mass * acceleration newtons (N) net force is 0 at equilibrium (at rest)
an impulse has good time resolution, but poor frequency resolution. true or false and justify your answer.
True, due to time-frequency trade off.
if you are interested in understanding the true level of a sound you can use ___ weighting in a sound level meter, but if you are interested in understanding how this sound level may impact humans you can use ___ weighting in a sound level meter when making these instruments.
Z; A
what is sound?
a longitudinal wave generated as a result of SHM of air particles which transports energy as a wave in a medium that has stiffness and mass.
sound level meters
allows for measurement of "sound pressure" in dB SPL (in air)
narrowband filter
allows frequencies between lower (f1) and upper (f2) cut-off frequencies
notch filter
allows frequencies outside lower (f1) and upper (f2) cut-off frequencies
high-pass filter
allows high frequencies above the cut-off frequency (fc)
low-pass filter
allows low frequencies below the cut-off frequency (fc)
time-frequency analysis
allows us to visualize both time and frequency information of a signal. ex: spectrogram
aperiodic signals lack harmonicity. what is one example of an aperiodic signal and explain why they lack harmonicity?
an example is white noise, it lacks harmonicity because the frequency is not in phase.
which of the following describes the purpose of Fourier transform?
b. breaks down a waveform into frequency component
peak amplitude
baseline to peak amplitude
good resolution
being able to see a really fine/narrow signal in either time or frequency domain
fine structure
carrier frequency waveform component
Fourier transform
decomposes a waveform into its constituent frequency components; when a signal is plotted as a spectrum
sound behavior in rooms
empty room= more reverberation than room with people, because people and clothes absorb sound more reverberation is good for concert halls
root mean square (RMS) amplitude
formula to obtain an average amplitude for the waveform; critical for pressure signals because they have both + and - values. Simple averaging will result in an artificial zero
simplest periodic complex sound is:
harmonic complex, which contains multiple harmonics fundamental frequency is the first harmonic
what is the difference between noise and impulse?
impulse's frequency components add in-phase, whereas the phase of noise is random
when a spring is in motion it has primarily ___ energy, and when it is extended or compressed it primarily has ___ energy.
kinetic; potential
complex and aperiodic sounds
made up of broad bands of frequencies; envelope of wave is horizontal line connecting all frequencies; continuous spectrum lacks harmonicity
what does resonance depend on?
mass and stiffness higher mass=lower frequency higher stiffness=higher frequency f=square root of (k/m)
envelope
modulator frequency waveform component
how can we module the amplitude of a signal? (AM)
multiplying a lower frequency signal (modulator) with a higher frequency signal (carrier). this is called amplitude modulation. this will produce two waveform components in the same signal: the envelope and the fine structure. the spectrum of this signal will show the original carrier frequency (fc) and modulator frequenncy (fm) as two side bands fc+fm and fc-fm around the carrier frequency,
is it possible to add dB SPL and dB IL directly? why or why not?
no, because they are two different logarithms. to add both values, we must convert both to the same dB form in a linear scale, add the measured values, and then convert back to a log scale.
what are some examples of resonators in the body?
oral cavity and nasal cavity, the sinuses
in no more than 2 sentences, describe the relationship between frequency and period
period and frequency are inversely related (p=1/f). frequency is how many cycles per second, where period is how many seconds per cycle/sine wave.
2 forms of energy
potential and kinetic
waveforms and spectra
provide different information about the same sound signal
2 extremes of time-frequency trade off
pure tone- great frequency resolution but poor time resolution impulse- great time resolution but poor frequency resolution
scalar quantity
quantities only with magnitude
vector quantity
quantities with magnitude and phase
2 types of quantities
scalar, vector
filters
selective barriers that allow relevant things (signal) to pass through while blocking irrelevant things (noise). 4 main types: 1. low pass 2. high pass 3. narrowband 4. notch
skirts
sharp/clean rectangular shape in the frequency domain means that these filters will have poor time-domain response, meaning they will add additional unwanted signals into our desired signal. to avoid this we expand the filtering regions around the rectangle=skirts
is sound a longitudinal or transverse wave? what does that mean?
sound is a longitudinal wave. that means that sound disturbed the medium that transports energy without permanently transporting matter. the particles do not travel with the wave.
integer number
successive harmonics are related to the fundamental by this and the fundamental frequency
what does negative dB mean?
that the measured intensity or pressure (Ix, px) is smaller than the reference intensity or pressure (Iref, pref)
potential energy
the energy that the object expends when it is at rest stiffness is the ability of objects to store potential energy, as it is the stiffness of the spring in the spring-mass system that stores all the energy when we deform it
what does it mean when the net force is 0?
the object is at rest, or equilibrium
quantify skirts by:
their slope, or roll-off how many dB does the filter attenuate per octave
simple harmonic motion (SHM)
vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium think about compressing a spring and letting it engage in SHM at rest (potential)>apply external force and displacing (restoring force generates and potential transforms to kinetic)>rest (potential)>external force is removed (restoring force takes over)>repeats over and over because it shoots past equilibrium define using sine function- displacement as a function of time x(t)= A * sin(2*π*f*t + Φ) π= instantaneous phase of the displacement f= frequency, or how fast displacement is happening t= different time points of displacement A= amplitude of displacement Φ= initial/starting phase
complex sounds
vibrations that contain two or more frequencies (multiple sine waves)
sound intensity and sound pressure are proportional as I ∝ p^2. what can we infer about the relationship between dB IL and dB SPL based on this relationship?
we can infer that intensity and pressure are the same/directly proportional when pressure is raised to the second power. So when intensity is raised 100 fold, pressure will be raised 10 fold.
what is a drawback of spectrum?
we lose all the valuable time information when we go from time to frequency domain using Fourier transform. we can overcome this drawback by performing time-frequency analysis.
explain why we need root-mean-square to represent sound pressure.
we need root-mean-square to obtain an average amplitude for the waveform, which is critical for pressure signals due to their positive and negative values.
harmonicity
when a sound is called periodic; the frequency components of a signal are related in an orderly fashion
what is an example of an aperiodic complex sound?
white noise impulse
difference between AM and FM signals
-FM produces a lot more sidebands than AM -AM envelope changes with time but the fine structure stays constant
what 5 parameters can define simple harmonic motion (SHM)?
1. amplitude 2. frequency- how many cycles are there in 1 second 3. period- inverse of f; time period of sine wave 4. wavelength- c/f 5. phase
how do you add dB values?
1. convert dB (which is in log scale) to linear scale 2. add it in the linear scale 3. convert back to log scale if sources are the SAME: IL: dBx + 10log(N) SPL: dBx + 20log(N) N=number of sources dBx=level of the signals that need to be added
if the upper sideband of a 1000 hz amplitude modulated signal is 1100 hz, what is the modulation frequency?
100 hz, because both lower and upper sidebands are symmetrically separated around the carrier frequency by the modulation frequency. therefore, 1100 (upper sideband) - 1000 (carrier) = 100 hz (modulation frequency
what weighting is used in sound level meters to mimic human hearing?
A weighting
octave is ___ in frequency
doubling question 9 assignment 2
what force allows objects to get back to their original position in simple harmonic motion? where is this force generated? explain the law that defines this force.
restoring force- ability to return to a normal shape after experiencing distortion generated in the spring Hooke's law defines this: F=-k*x
if intensity goes up 10 fold, what is the resulting increase in dB IL?
square root of 10-fold
if there are sounds of the same frequency traveling in opposite directions, they create:
standing waves, which creates peaks and valleys at different frequencies depending on the resonance of the cavity
why is stiffness considered the ability of objects to store potential energy?
stiffness of the spring in the spring mass system stores all the energy when we deform it
kinetic energy
the energy that the object expends when it is in motion mass is the ability of the objects to store kinetic energy, as mass resists any motion due to inertia, which must be overcome to set an object in motion
fundamental frequency
the lowest frequency of vibration of a standing wave; spacing between harmonics ex: two frequency components of a harmonic complex: 800 hz and 1000 hz, what is the fundamental frequency of this complex wave? A: 200 hz
the SHM equation describes displacement as a function of ___. the result can be described pictorially as a ___.
time; sine/longitudinal wave
in the space below, write out the equation we use for SHM/sound and label what the variables mean.
x(t)= A * sin(2*π*f*t + Φ) π= instantaneous phase of the displacement f= frequency, or how fast displacement is happening t= different time points of displacement A= amplitude of displacement Φ= initial/starting phase
if the distance from a source is moved 6 times farther away, what is the intensity level at the new location?
-6 per doubling -6x3= -18
sound intensity level (IL)
-Iref= 10^-12 W/m^2 -units: dB IL -formula: dB IL = 10*log(Ix/Iref)
if we have 3rd and 4th harmonic of a harmonic complex: 900 hz and 1200 hz, what are the first two harmonics of this complex wave?
1200-900= 300 (1st harmonic) 300x2= 600 (2nd harmonic)
if the signal level is 80 dB SPL and the noise level is 65 db SPL, what is the signal to noise ratio?
80-65= 15 SNR
in a few sentences, describe what it means for a signal to have good frequency resolution. is it possible for a signal to have both good frequency resolution and good time resolution?
For a signal to have good frequency resolution, it means it has a fine/narrow line, meaning there is a lack of uncertainty in what the frequency content of the signal is. It is impossible for a signal to have both good frequency resolution and good time resolution due to the time frequency trade-off, meaning you only get one or the other.
complex and periodic sounds
Have a dominant frequency with multiple variable frequencies (sine waves) has harmonicity
internal force
Hookian- restoring force force (F)- developed by a spring when it is deformed F= -k * x (k=stiffness constant) Work done= F * deltaX (work is done when the applied force moves an object) Energy= F* deltaX
if intensity increases 100-fold, what are the resulting dB IL and dB SPL values? assume reference value is 1.
I ∝ p^2 100 = p^2 square root 100 = 10 (when intensity increases 100-fold, pressure will go up 10-fold) dB = 10*log(Ix/Iref) dB = 10*log(100/1) = 20 dB dB = 20*log(px/pref) dB = 20*log(10/1) = 20 dB *note that answers are in dB because we used a reference value other than 10^-12 and 20x10^-6 Pa
how are intensity and pressure related?
I ∝ p^2 or p ∝ square root of I dB IL will ALWAYS BE EQUAL to dB SPL
how can we quantify overall amplitude?
1. peak amplitude 2. peak to peak amplitude 3. root mean square (RMS) amplitude
how can sound be quantified?
1. sound power 2. sound intensity 3. sound pressure
if the period of a sine wave is 1000 ms, what is its frequency?
1000 ms= 1 second. 1= 1/f f= 1
if pressure goes up 10 fold, what is the resulting increase in dB SPL?
10^2: 100-fold
derived quantities
-displacement (x) in meters (m) -velocity (v)- rate of change of displacement in (m/s) -acceleration (a)- rate of change of velocity in (m/s^2)
sound pressure (p)
-force acting per unit area -units: N/m^2 -dependence on distance (r) depends based on simple reciprocal (1/r)
three fundamental quantities that define simple harmonic motion
-mass (M) in kilogram (kg) -length (L) in meters (m) -time (T) in seconds (s)
sound power (P)
-output power of the source -units: Watts (W) -no dependence on distance (r) of measurement from the source; it is the property of the source
sound power level (SWL)
-pref= 10^-12 W -units: dB SWL -formula: dB SWL = 10*log(Px/Pref)
sound pressure level (SPL)
-pref= 20*10^-6 Pa -units: dB SPL -formula: dB SPL = 20*log(px/pref)
sound intensity (I)
-sound power passing through unit area -units: W/m^2 -dependence on distance (r) depends based on inverse-square law (1/r^2)