mteb/BrightProPsychologyRetrieval huggingface dataset:
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11. The Psychology of Shapes
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One of the possible molecular pathways guiding the structural maturation of
the BM seems to involve emilin2, expression of which starts around the time of
birth, peaks around P15 (17) and is observed throughout the life span,
suggesting that it is a constitutive member of the BM. Interestingly, the
emilin2  -/-  BM shows a more braided pattern of fibers than in the control
animals, even at P10, when lower levels of emilin2 are detected in the BM (  
17 .") , Fig.  5
 B), compared to more mature stages (P20,
P180), when the phenotype is also more pronounced (Fig.  5
 ).
Number of occurrences or cycles per unit time
Main article:  Utility frequency
In  SI base units   |   s  −1
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Time:  2024/03/30 17:17:38
f  =  1  T  .  {\displaystyle f={\frac {1}{T}}.}
Frequency is an important parameter used in science and engineering to specify
the rate of  oscillatory  and  vibratory
 phenomena, such as mechanical vibrations, 
audio signals  (  sound  ),  radio waves  , and  light
 .
* 
*  Spectrogram
For example, if a heart beats at a frequency of 120 times per minute (2
hertz), the period—the interval between beats—is half a second (60 seconds
divided by 120  beats  ).
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Tomomi Tani
Modern frequency
counter
For periodic waves in  nondispersive media  (that is, media in which the wave speed is independent
of frequency), frequency has an inverse relationship to the  wavelength
 , _λ_ (  lambda  ).
Even in dispersive media, the frequency _f_ of a  sinusoidal wave
 is equal to the  phase velocity
 _v_ of the wave  divided
 "Division \(mathematics\)") by the wavelength
_λ_ of the wave:
Diagram of
the relationship between the different types of frequency and other wave
properties. In this diagram, _x_ is the input to the function represented by
the arrow.
BM fibers become more misaligned and twisted in _Emilin2_ −/−  mice to
compared to wild type BM. ( **A** ) Histograms of BM fiber orientation as
function of developmental stage (P10, P20 to P180) for measurements in the
apical (top row) and basal (bottom row) cochlea regions. Fiber orientations
were assigned to 10° bins. The mean orientation in each preparation was
normalized (to ~ 101°) and the resultant histograms were fitted with normal
distribution curves. Table  2  lists SD
from the mean. Groups, three mice (six cochleae); differences in SD, ** _p_ <
0.0001, _F_ test statistics. Fiber orientations for the apical turn were
measured from optical Sects. (0.5 μm apart in 8 optical sections). Measurement
numbers for each developmental age: P10 n = 90,001; P10  -/-  n = 53,920 ; P20
n = 163,805 ; P20  -/-  n = 164,805;P 180 n = 166,203; P180  -/-  n = 167,203
; using BM samples from six cochleae (3 mice) per age group. Fiber
orientations measured for the basal turn(bottom row) were measured from
optical Sects. (0.5 μm apart in 20 optical sections). Measurement numbers for
each developmental age: P10 n = 283,742; P10  -/-  n = 27,246; P20 n =
145,339; P20  -/-  n = 151,419; P180 n = 147,231, P180  -/-  n = 149,250 using
BM samples from six cochleae (3 mice) per age group. ( **B** ) Birefringent
images constructed from optical stacks of transverse sections taken through
the pectinate zone of the BM have less homogeneous and more braded appearance
with increasing stages of development in emilin  -/-  compared to emilin  +/+
BM. Transversal (plane _pl_ in Fig.  3 
E) filament array images reconstructed from stacks of pectinate zone optical
sections for P10, P20 and P60 emilin  +/+  and emilin  −/−  cochleae (0.5 μm
apart; 8 apical and 18 middle optical sections; total thicknesses are 4 and 9
μm, respectively). Scale bar 5 μm.
##  Definitions and units
Message ID:  922505476
**Figure 3**
A 
pendulum  with a period of 2.8 s and a frequency
of 0.36  Hz
To better understand the dynamics of BM structural development in the
pectinate zone of the BM (Fig.  1  A), a
detailed analysis of BM structural organization was performed from the day of
birth (P1) until 6 months old, where P20 is the time of hearing onset in mice
(Fig.  2  ). The arbitrary orientation of
BM sections in each preparation resulted in color differences between
preparations (Fig.  2  A,B). To
facilitate the comparions between samples, image X axis was used as zero
degree for the fibers that are aligned along Y axis. Within a given
preparation, the slow axis orientation, as reflected in the pseudocolor coded
presentations of optical axis of orientation, varied along the tonotopic axis
for the preparations < P15, indicating disarrangement of fibers in the early
stages of postnatal development (Fig.  2 
A,B showing apical and basal ends for comparison). The colors became more
uniform in preparations over ~ 10 days of age, indicating that the fiber
orientation was more uniform at older stages (Fig.  2
 A,B). In the apical region, only fibers
could be observed, while fiber bundles were dominant in the more basal
regions. These observations are consistent with the relatively sparse presence
of collagenous filaments in apical compared to mid-basal regions of the BM, as
shown by electron microscopy   9 . Z. Zellforsch. Mikrosk. Anat. 56, 40–96 \(1962\).") ,  10
.") .
A  pendulum  making 25 complete  oscillations
 in 60 s, a frequency of 0.41  6   Hz
Article   PubMed

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*  Keyboard frequencies = naming of notes – The English and American system versus the German system 
*  A frequency generator with sound, useful for hearing tests
The unit of angular frequency is the  radian  per second (rad/s) but, for  discrete-time signals  , can also be expressed as radians per  sampling interval  , which is a  dimensionless quantity  . Angular frequency is frequency multiplied by 2  π  .
Portal  :
**Aperiodic frequency** is the  rate  "Rate
\(mathematics\)") of incidence or occurrence of non-  cyclic
 phenomena, including random
processes such as  radioactive decay  . It is expressed with the  unit  of  reciprocal second  (s  −1  )  [14]  or, in the case of radioactivity,  becquerels
 .  [15]
The authors would like to thank Douglas Forrest at NIDDK (NIH) for providing
samples of emilin2  -/-  cochlea, Rudolf Oldenbourg at the MBL, Woods Hole, MA
for providing facilities and training for optical imaging, Milos Stankovic for
providing the Figures  1  A,  3
 F and supplementary movie, and George
Burwood, Ian Russell, Andrei Lukashkin and Rudolf Oldenbourg for providing
critical comments to earlier versions of the manuscript.
Therefore, it is imperative to fully understand the composition of BM, how it
changes with development, maturation and different pathological states along
the tonotopic axis and to explore the only partially understood roles of the
BM and ECM. Together, this information will further our understanding of ECM-
cell interactions mediating hearing functions, which is of utmost importance
for understanding the structural contributions BM plays in the OC development
and the transduction of the auditory signals. A better understanding of how
the BM and ECM regulates organ structure and function and how the BM and ECM
remodeling affects auditory processing will potentially contribute to the
development of new therapeutics   63 .") .
###  Counting
In  dispersive media  "Dispersion \(optics\)") ,
such as glass, the speed depends somewhat on frequency, so the wavelength is
not quite inversely proportional to frequency.
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The  sound wave  spectrum, with rough guide
of some applications
Article
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See also:  Frequency meter
A remarkable feature of the basal, high frequency, cochlea region of altricial
mammals, which occurs in the third week of development, is the upward shift in
the frequency of the tone most effective in eliciting gross cochlear
potentials  19  ,  20  ,  21 .") . Moreover, auditory nerve responses become more
sensitive and sharply tuned   22 .") ,  23
.") .
Neural frequency tuning originates as a consequence of BM vibrations   1
.") ,  3 .") and the developmental upward frequency shift in
the tonotopic neural frequency map of the cochlea has been demonstrated to be
associated with an upward shift in the BM vibration frequency map  24  ,  25
,  26 .") . Concomitantly, the cochlear partition in the basal turn of the
cochlea becomes stiffer   27 .") . Developmental
change in stiffness of the cochlear partition could involve changes in several
structures. For example the dimensions of the organ of Corti and thickness of
the radial fibre bands of the BM increase during development consistent with
the upward shift in the BM frequency, such as increases in the thickness of
the radial fibre bands within the BM frequency map   22
.") ,  28
.") . There is also a developmental increase in the density
of proteoglycans   29 .") ,
increased proliferation of tension fibroblasts in the spiral ligament   22
.") ,  30
.") and maturation of the
pillar cells of the organ of Corti   31 .") .
*  John Backus  "John Backus \(acoustician\)")
*  Jens Blauert 
*  Ernst Chladni 
*  Hermann von Helmholtz 
*  Carleen Hutchins 
*  Franz Melde 
*  Marin Mersenne 
*  Werner Meyer-Eppler 
*  Lord Rayleigh 
*  Joseph Sauveur 
*  D. Van Holliday 
*  Thomas Young  "Thomas Young \(scientist\)")
Our study focused on development (up to 1 month old), and included animals 6
month old, when the onset of age related age hearing loss has been reported.
Namely, studies investigating age related hearing loss in C57B/J animals using
the auditory brainstem response (ABR) test, showed the hearing threshold
levels of the mice increased progressively starting at about 6 months of age,
significantly worsening by 15 months of age  50  ,  51  ,  52
.") . Moreover, the observed decrease in the characteristic frequency
would be expected with decline of the aging cochlear amplifier but decline in
the amplification even in C57B/J mice is, probably, a complex process (i.e.
not only changes in the BM morphology which still can contribute though) with
contribution from strial atrophy and EP decline   53
.") .
Chengxiang Qiu, Beth K. Martin, … Jay Shendure
d  θ  d  x  =  k  =  2  π  ξ  .  {\displaystyle {\frac {\mathrm {d} \theta
}{\mathrm {d} x}}=k=2\pi \xi .}
4. Michael Shribak
Further information:  Wave propagation
The  SI  unit of frequency is the  hertz  (Hz),  [4]  named after the German physicist  Heinrich Hertz
 by the  International
Electrotechnical Commission  in 1930. It was adopted by the 
CGPM  (Conférence générale des poids et mesures) in 1960,
officially replacing the previous name, _ cycle per second
 _ (cps). The SI unit for the
period, as for all measurements of time, is the  second  .  [5]  A traditional unit of frequency used with rotating
mechanical devices, where it is termed _ rotational frequency
 _ , is  revolution per
minute  , abbreviated
r/min or rpm.  [6]  60 rpm is equivalent to one hertz.  [7]
##  Materials and methods
Low: 1kHz
Animations by S. Blatrix and G. Rebillard
*  Pitch  "Pitch \(music\)")
*  Bark scale 
*  Mel scale 
*  Equal-loudness contour 
*  Fletcher–Munson curves
###  Sound
Snezana Levic
Article   CAS   PubMed

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An old method of measuring the frequency of rotating or vibrating objects is
to use a  stroboscope  . This is an intense
repetitively flashing light (  strobe light  ) whose frequency can be adjusted with a calibrated timing circuit.
The strobe light is pointed at the rotating object and the frequency adjusted
up and down. When the frequency of the strobe equals the frequency of the
rotating or vibrating object, the object completes one cycle of oscillation
and returns to its original position between the flashes of light, so when
illuminated by the strobe the object appears stationary. Then the frequency
can be read from the calibrated readout on the stroboscope. A downside of this
method is that an object rotating at an integer multiple of the strobing
frequency will also appear stationary.
Article   ADS
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###  Line current
Sound propagates as mechanical vibration waves of pressure and displacement,
in air or other substances.  [11]  In general, frequency components of a sound
determine its "color", its  timbre  . When speaking
about the frequency (in singular) of a sound, it means the property that most
determines its  pitch  "Pitch \(music\)") .  [12]
##  Aperiodic frequency
Correspondence to  Snezana Levic  .
c  =  f  λ  ,  {\displaystyle \displaystyle c=f\lambda ,}
Article  Open access  14 February 2024
2. Maki Koike-Tani
1. Tomomi Tani
In the  special case  of electromagnetic
waves in  vacuum  , then  _v_ = _c_ , where _c_ is
the  speed of light  in vacuum, and
this expression becomes
The BM is a specialized layer of extracellular matrix (ECM) sandwiched between
the overlying sensory epithelium, containing the sensory hair cells and
supporting cells, and an underlying layer of tympanic border cells   6
 44–129 \(Springer,
New York, 1996\).") . BM structural components are most probably secreted from
the underlying mesothelial cells   7 .")
,  8 .") . Early
anatomical studies using electron microscopy revealed that the mature BM is
composed of radial collagenous filaments, 10–12 nm in diameter, embedded in a
matrix of ground substance  9  ,  10  ,  11
.") . The BM filaments are
composed primarily of laminin-β2 and collagen types II and IV  12  ,  13  ,
14  ,  15  ,  16 .") . The collagenous fibers have been associated with several
glycoproteins, including Fibronectin and Tenascin   16
.") . More
recently, Emilin2 was identified in the BM   17
.") and was shown to affect collagen
fibril arrangement, and thereby to affect its elastic properties and frequency
tuning bandwidth   18 .")
. This finding agrees with the generally accepted mechanical basis of
frequency tuning in the cochlea that depends on the apical basal stiffness
gradient of the BM which, in turn, depends largely on its structural
organization   1 .") ,  3
.") .
A resonant-reed frequency meter, an obsolete device used from about 1900 to
the 1940s for measuring the frequency of alternating current. It consists of a
strip of metal with reeds of graduated lengths, vibrated by an  electromagnet
 . When the unknown frequency is applied
to the electromagnet, the reed which is  resonant  at that frequency will vibrate with large amplitude, visible next
to the scale.
Main article:  Audio frequency
##  Period versus frequency
See also:  Frequency (disambiguation) 
"Frequency \(disambiguation\)") and  Category:Units of frequency
Audio frequency  and  pitch
 "Pitch \(music\)") |
Main articles:  Light  and  Electromagnetic radiation
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---
 Acoustical engineering  |
_Scientific Reports_  ** volume  11 ** , Article number:  7581  (
2021  )  Cite this article
1. ** ^  ** The term _spatial period_ , sometimes used in place of _ wavelength  _ , analogously corresponds to the (temporal) period.  [9]
Main article:  Frequency counter
*  Audio frequency 
*  Bandwidth (signal processing)  "Bandwidth \(signal processing\)")
*  Chirp 
*  Cutoff frequency 
*  Downsampling 
*  Electronic filter 
*  Fourier analysis 
*  Frequency band 
*  Frequency converter 
*  Frequency domain 
*  Frequency distribution 
*  Frequency extender 
*  Frequency grid 
*  Frequency level 
*  Frequency modulation 
*  Frequency spectrum 
*  Interaction frequency 
*  Least-squares spectral analysis 
*  Natural frequency 
*  Negative frequency 
*  Periodicity (disambiguation)  "Periodicity \(disambiguation\)")
*  Pink noise 
*  Preselector 
*  Radar signal characteristics 
*  Signaling (telecommunications)  "Signaling \(telecommunications\)")
*  Spread spectrum 
*  Spectral component 
*  Transverter 
*  Upsampling 
*  Orders of magnitude (frequency)  "Orders of magnitude \(frequency\)")
Mai Thi Tran
Together, these results provided evidence that the collagenous fibers become
more compact and tightly aligned as development progressed, and that the
alignment of fibers was preserved through the length of the BM   43
.") . This is the
first study which demonstrates the developmental changes in 3D BM structure.
The mature BM form resembles a structure analogous to that of an airplane
wing, composed of many vertical ribs that align perpendicular the length of
the wing, which give some flexibility for the deflection of the wing while
maintaining mechanical strength (Fig.  3 
F, Supplementary movie).
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Moreover, in the apical region, fiber thickness increased progressively and
spacing of fibers reduced with development (Fig.  2
 C, D), reaching maturity around P20. A
similar trend was observed in more basal regions of the BM, where bundles of
fibers became thicker and more closely packed with maturation, reaching a
mature form by P20 (Fig.  2  E,F).
* Accepted  :  16 March 2021
In many media, such as air, the  speed of sound  is approximately independent of frequency, so the wavelength of the
sound waves (distance between repetitions) is approximately inversely
proportional to frequency.
*  Architectural acoustics 
*  Monochord 
*  Reverberation 
*  Soundproofing 
*  String vibration 
*  Sympathetic resonance
Derivations from
other quantities
BM provides structural environment that could determine mechanical properties
of the cells within the sensory epithelium. Moreover, the immediate mechanical
and electrical environment might have a significant role in controlling the
maturation and frequency-dependent properties of the cellular elements of the
OC. There are a few studies which demonstrate that maturation of IHCs and
their efferent innervation depend on mechanotransduction   77
.") ,  78 , 151–170 \(2020\).") . Because
mechanotransduction depends on the immediate mechanoelectrical environment of
HCs, including properties of the developing BM, it is sensible to suggest that
developing local mechanical properties and tonotopy of the BM is an important
part of the cochlear maturation. There is also an evidence that mechanical
forces drive ordered patterning of hair cells in the mammalian inner ear and
changes in the BM mechanical properties must be a crucial player here   79
.") . Thus, it may not be a pure coincidence that the
tonotopicity of cochlear cellular elements and parallels that of the BM   41
.") ,  80  ,  81  , 
82 .") . Moreover, the
tonotopicity is probably not entirely governed through genetics but is also
influenced by the local electromechanical environment. For example, the
maturation of mechanoelectrical transduction in IHCs is determined by
experiencing mechanical stimulation   77 .") .
This study is the first to provide direct evidence of the 3D structural
development and maturation of mammalian BM, which was hypothesized to underlie
the developmental maturation of tonotopic maps and frequency tuning in animal
models   22 .") ,  23
.") ,
 26 .")
,  28 .") ,  44  ,  45  ,  46
 9, 22–32 \(2008\).") as well as in newborn humans
 47 .") . The results of this study show an
increase in fiber thickness and more compact ordering with maturation (Figs. 
1  and  2
 ). The fibers in the early period of
maturation ( _p_ < 15) show a wavier pattern, however, they seem to be aligned
throughout the BM, without the braiding pattern observed in the emilin2  −/−
(Figs.  3  and  5
 , Supplementary Fig.  3
 ). Moreover, there is a temporal delay
in maturation, with the apical cochlear region lagging behind the basal
region, consistent with the general maturation of the OC (reviewed in   48
.") ). Thus, BM structural maturation
is temporally coupled to the maturation of hearing (reviewed in   49
.") ).
###   Local origin of excitatory–inhibitory tuning equivalence in a cortical
network
CAS   PubMed

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###  Publisher's note
The BM is an example of an ECM, which is a highly dynamic, three-dimensional
acellular structure that is present in all tissues and is essential for life
 74 .") . The ECM is shown to provide
structural support, cell adhesion and to play a vital role in the
determination, differentiation, proliferation, survival, polarity, and
migration of cells in many tissues, including central nervous system   75
.") .
Therefore, the ECM signals generated by the BM may be important in guiding the
normal development and functioning of the OC and are likely to be involved in
regulating development and cellular differentiation and signaling in the OC
throughout the life of the animal   76 .") .
####  _The methods are similar to the ones used by Russell_ et al. _2020_  18
.")
**Figure 4**
Differences in structural alignment of the developing BM and quantification of
how the fibers were extended or/and twisted (Fig.  3
 D,E) was determined by tracking the
optical axis orientations of the fibers through the BM volume (in longitudinal
transverse views through the pectinate zone , i.e. a cross-section defined in
Fig.  3  C). The fibers are more twisted
and braided earlier in development (< P15, Fig.  3
 . However, as the BM matures, the fibers
become more aligned. The images shown in Fig.  3
 D,E represent a unique structure of
extracellular matrix (ECM) in the BM which, in its mature form, looks like an
alignment of flat sheets of extracellular matrix that run perpendicular to the
length of the BM. A schematic representation summarizing the main observations
of BM structural development is shown in Fig.  3
 F and Supplementary movie.