Conversion of sone to phon and the problem with
The subjective perceived sound volume and the artificial term loudness are
subjective terms trying to describe the strength of the ear's perception of a sound.
The determination of the loudness of stationary signals is defined in ISO 532 or in DIN 45631.
The loudness of
N = 1 sone is equivalent to 40 phons, which is the loudness level
of LN = 40 dB of a sine wave (sinusoid) with a frequency of f = 1000 Hz.
Kurt Tucholsky: &Noise is the noise of others and one's dog makes no noise.&
&There are many kinds of noise - but only one silence.&
Loudness is a personal subjective characteristic of a sound - as opposed to the
sound pressure level in decibels, which is objective and directly measurable. SPL.
(Magnitude of Sound):
LN (phons) to Loudness N (sones)
N (sones) to Loudness level
LN (phons)
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Conversion valid between 40 phons and 120 phons
That means for larger values than '1 sone is equal to 40 phons'
 Loudness level LN 
phons 
 | 
Loudness N  
sones 
 For LN & 40 phon 
 | 
 For N & 1 sone 
        ↓
 | 
                 ↓
 | 
Loudness N  
soens 
 | 
 Loudness level LN 
phons 
 | 
     
For loudness level LN & 40 phons: loudness N in sones = 2[(LN & 40)/10]      (LN in phons)
For loudness N & 1 sone: loudness level LN in phons = 40 + [10 & log N / log102]      (N in sones)
log 2 = 0.30103          LN in phons = 40 + 33.22 & log N          N in sones
Conversion only valid between 8 phons and 40 phons
That means for smaller values than '1 sone is equal to 40 phons'
Loudness level LN 
phons 
 | 
Loudness N  
sones 
 Only for LN & 40 phon 
 | 
 Only for N & 1 sone 
       ↓
 | 
       ↓
 | 
Loudness N  
sones 
 | 
 Loudness level LN 
phons 
  
For loudness level LN & 40 phons: loudness L in sones = (LN / 40)2.86 & 0.005           LN in phons
For loudness N & 1 sone: loudness level LN in phons = 40 & (N + 0.0005)0.35            N in sones
According to Stanley Smith Stevens' definition, 1 sone is equivalent to 40 phons,
which is defined as the loudness level of a pure 1 kHz tone at LN = 40 dBSPL,
but only (!) for a sine wave of 1 kHz and not for broadband noise.
There is no &dBA& curve given as threshold of human hearing. &dBA& has
absolutely noting to do with sone, or with phons, or sound pressure level in dB.
60 phons means "as loud as a pure 1000 Hz tone with a level of 60 dB."
Relation between loudness N in sones
and loudness level LN in phons
 phons 
 sones 
N (sone) and loudness level
LN (phon), as shown
here, is easily converted into one another. But the
psychoacoustic perceived loudness level and the objectively
measured sound pressure level in dBSPL cannot be converted
to the weighted dBA level. There is no formula.
The typical question: &How to convert 0.5 sone to decibel (dB)?&
cannot be answered. Only a pure tone of 1 kHz measured in phons is
equivalent to a dB-SPL value.
Distinguish carefully when looking at the volume (magnitude of sound).
Sone is part of the loudness. Phon is part of the loudness level.
Try to avoid the laymen's word &intensity&.
dB or dB-SPL is the sound pressure level.
dBA is a filter measurement for a very simplified evaluation of volume.
The volume of a sound is a subjective perception. To "measure" loudness,
the volume of a 1,000 hertz reference tone is adjusted until it is perceived by
listeners to be equally as loud as the sound being "measured". The loudness
level, in phons, of the sound is then equal to the sound-pressure level, in
decibels. Readings of a pure 1 kHz tone should be identical, whether
weighted or not.
Between the loudness N in sone and the loudness level LN in phon we have
the following connection (ISO-recommendation ISO/R 131-1959):
Loudness N = 2(LN & 40)/10 or loudness level LN = 40 + 10 & lb N.
"lb" means logarithm base 2.                  10 & lb N = 10 & log2(N)
The sone is a unit of perceived loudness after a proposal of Stanley Smith
Stevens () in 1936. In acoustics, loudness is a subjective measure
of the sound pressure. One sone is equivalent to 40 phons, which is defined
as the loudness of a 1 kHz tone at 40 dBSPL. The number of sones to a phon
was chosen so that a doubling of the number of sones sounds to the human
ear like a doubling of the loudness, which also corresponds to increasing the
sound pressure level by 10 dB, or increasing the sound pressure by a ratio
3.16 (= &10). At frequencies other than 1 kHz, the measurement in sones
must be calibrated according to the frequency response of human hearing,
which is of course a subjective process.
The study of apparent loudness is included in the topic of psycho acoustics.
Volume in acoustics is used as a synonym for loudness. It is a common term
for the amplitude or the level of sound.
To be fully precise, a measurement in sones must be qualified by the optional
suffix G, which means that the loudness value is calculated from frequency
groups, and by one of the two suffixes F (for free field) or D (for diffuse field).
Note - Comparing dB and dBA: There is no conversion formula for
measured dBA values to sound pressure level dBSPL or vice versa.
There is no correlation between sound pressure level SPL as broadband
measuring and dBA. To know the measuring distance
and the frequency content of the signals could also be important.
With the following table you can try to convert roughly, but be cautious using
these psychoacoustic values. The frequency composition of the signal
amplitude is always unknown. The distance of the measuring point is
important for the value of the measure.
From a dB-A measurement no accurate description of the expected volume
is possible.
A typical noise question: How does dbA compare to sones?
The following chart is, however, for the dBA values no accurate
knowledge & it's more a guess.         &Conversion& of &sones to dBA&
This frequency weighting with the A-curve is used for noise
measurements. It is close to the frequency response of the human
hearing for levels below 40 dB only. But this filter is also used for
higher levels, a purpose it was never intended for, and is not
suited to, and therefore gives lower test results than our ears are
hearing. The cut-off low frequencies are not measured.
A formula with a cautious try to convert sones to decibels:
dBA = 33.22 & log (sones) + 28 with a possible accuracy of & 2 dBA
or sones = 10^[(dBA & 28) / 33.22]
The phon is a unit of perceived loudness level, which is a subjective measure
of the strength (not intensity) of a sound. At a frequency of 1 kHz, 1 phon is
defined to be equal to 1 dB of sound pressure level above the nominal
threshold of hearing, the sound pressure level SPL of 20 &Pa (micropascals) =
2&10&5 pascal (Pa). Our ears as sensors cannot convert sound intensities and
powers, they can only use the sound pressure changes between 20 Hz and
20,000 Hz. At other frequencies, the phon departs from the decibel, but is
related to it by a frequency weighting curve () that
reflects the frequency response of human hearing. The standard curve for
human hearing is the A-weighted curve (the equal-loudness contour for a 40
dB stimulus at 1 kHz), but others are in use.
The "unit" phon has been largely replaced by the dBA (A-weighted decibel),
though many old textbooks and instructors continue to use the phon.
Note: &Set the volume of the radio double as loud or half as loud.& Who does
not know, how to do this, is a normal person. Psycho-acousticians are telling
us, that it has to be 10 dB level difference. Try to cool your hot coffee to the
point &half as hot& - and think it over. Your own feeling may be much different
to other persons.
An increase from 6 dB to 10 dB is perceived by most listeners as &double& the
volume. These sensations are highly subjective, meaning that different people
will hear this in different ways, and &twice as loud& is a much harder thing to
guess than something.
The human perception of loudness is perceived differently from each subject.
In other words it is one's own perception of sound and it is subjective of sound
pressure level SPL.
Incidentally, the sound pressure p doesn't decrease with the square of the distance
from the sound source (1/r²). This is an often-told and believed wrong tale.
Sound Level Comparison Chart with Factor
Table of sound level dependence and the change of the respective factor to subjective volume
(loudness), objective sound pressure (voltage), and sound intensity (acoustic power)
How many dB to appear twice as loud (two times)? Here are all the different factors.
Factor means "how many times" or &how much& ... Doubling of loudness.
Sound pressure
Acoustic Power
Sound Intensity
;    
0;     
   316     
0;   
100  
  8
   31.6
  4
        2.0 = double  
       3.16 = &10
  +6 dB
  1.52 times
 2.0 = double  
4.0  
  +3 dB
  1.23 times
1.414 times = &2
              2.0 = double  
  - - - - &0 dB - - - -
- - -1.0 - - - - - - - 
- - - - - 1.0 - - - - - - - 
- - - - - 1.0 - - - - - -
  &3 dB
    0.816 times
           0.707 times
         0.5 = half
  &6 dB
    0.660 times
      0.5 = half
0.5 = half  
0.1  
          0.25
          0.125
  0.0316
  0.001
          0.0625
  0.0100
     0.0001
          0.0312
  0.0032
       0.00001
          0.0156
 0.001
         0.000001
Log. quantity
Psycho quantity
Field size
Energy size
Loudness multipl.
Amplitude multiplier
Power multiplier
For a 10 dB increase of the sound level we require ten times more power from the amplifier.
This increase of the sound level means for the sound pressure a lifting of the factor 3.16.
Loudness and volume are highly subjective. That belongs to the domain of psychoacoustics.
Is 10 dB or 6 dB sound level change for a doubling or halving of the loudness (volume) correct?
About the connection between sound level and loudness, there are various theories. Far spread is still the
theory of psycho-acoustic pioneer Stanley Smith Stevens, indicating that the doubling or halving the
sensation of loudness corresponds to a level difference of 10 dB. Recent research by Richard M. Warren,
on the other hand leads to a level difference of 6 dB. *) This means that a double sound pressure
corresponds to a double loudness. The psychologist John G. Neuhoff found out that for the rising level our
hearing is more sensitive than for the declining level. For the same sound level difference the change of
loudness from quiet to loud is stronger than from loud to quiet.
It is suggested that the sone scale of loudness reflects the influence of known experimental biases and
hence does not represent a fundamental relation between stimulus and sensation.
Citation: When known experimental biases were eliminated, half loudness was equal to half sound
pressure level (&6 dB) from 45 to 90 dB.
It follows that the determination of the volume (loudness) which is double as loud should not be
dogmatically defined. More realistic is the claim:
A doubling of the sensed volume (loudness) is equivalent
to a level change approximately between 6 dB and 10 dB,
the psycho-acousticians are telling us.
There is a constant uncertainty of the answer to the question:
"How many dBs are doubling a sound"? or &What is twice the sound?&
Doubling the (sound) intensity is obtained by an increase of the sound intensity level of 3 dB.
Doubling the sound pressure is obtained by an increase of the sound pressure level of 6 dB ●
Doubling the loudness feeling is obtained by an increase of the loudness level of about 10 dB. 
Double or twice the power = factor 2 means 3 dB more calculated power level (sound intensity level).
Double or twice the voltage = factor 2 means 6 dB more measured voltage level (sound pressure level) ●
Double or twice the loudness = factor 2 means 10 dB more sensed loudness level (psycho acoustic).
Acoustics - Normal equal-loudness-level contours (ISO 226:2003)把5分之4:0.25化成最简整数比是(),比值是小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。甲数与乙数的比是9比4,甲数比乙数多()%甲数是乙数的1又5分之3,乙数与甲数的比是a.b都是不等于0的自然数,如果a*7=b*-中国学网-中国IT综合门户网站-提供健康,养生,留学,移民,创业,汽车等信息
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把5分之4:0.25化成最简整数比是(),比值是小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。甲数与乙数的比是9比4,甲数比乙数多()%甲数是乙数的1又5分之3,乙数与甲数的比是a.b都是不等于0的自然数,如果a*7=b*
来源：互联网 发表时间： 10:25:19 责任编辑：鲁晓倩字体：
为了帮助网友解决“把5分之4:0.25化成最简整数比是(),比值是小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。甲数与乙数的比是9比4,甲数比乙数多()%甲数是乙数的1又5分之3,乙数与甲数的比是a.b都是不等于0的自然数,如果a*7=b*”相关的问题，中国学网通过互联网对“把5分之4:0.25化成最简整数比是(),比值是小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。甲数与乙数的比是9比4,甲数比乙数多()%甲数是乙数的1又5分之3,乙数与甲数的比是a.b都是不等于0的自然数,如果a*7=b*”相关的解决方案进行了整理,用户详细问题包括:RT,我想知道:把5分之4:0.25化成最简整数比是(),比值是小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。甲数与乙数的比是9比4,甲数比乙数多()%甲数是乙数的1又5分之3,乙数与甲数的比是a.b都是不等于0的自然数,如果a*7=b*，具体解决方案如下：解决方案1： 有一个长方形与一个正方形周长相等,长方形的宽是长的5分之1，则长方形的面积与正方形的面积的比？解：设正方形的边长为单位”1“&则正方形的周长为： 1X4=4& & &长方形的周长为： &4&则长方形的长与宽的和为： 4÷2=2& 长方形的长与宽的比为： &1:1/5=5:1& 长方形的长为： &2÷（1+5）X5=10/6=5/3& &长方形的宽为： &2÷（1+5）X1=1/3& 长方形的面积为： &5/3X1/3=5/9& 正方形的面积为: &1X1=1& 长方形的面积与正方形的面积的比： &5/9:1=5:9答：长方形的面积与正方形的面积的比为5：9 补充： 把5分之4:0.25化成最简整数比是(),比值是解：4/5:0.25& & & =4/5:1/4& & & =4/5X20:1/4X20& & & =16:5& 再算比值：&& & & &4/5:0.25& & & =4/5:1/4& & & =4/5X20:1/4X20& & & =16:5& & & =3.2答：把5分之4:0.25化成最简整数比是(16：5),比值是（3.2） 补充： 小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。解：先算一下，小刚和小丽走的路程比： &（1+1/4):1=5:4& & &再算一下，小刚和小丽用的时间比： &1：（1+1/10)=10:11& & 再算一下，小刚和小丽的速度比： &5/10：4/11& & & & & & & & & & & & & & & & & & & & & & & & & & & & & =5/10X110:4/11X110& & & & & & & & & & & & & & & & & & & & & & & & & & & & & =55:40& & & & & & & & & & & & & & & & & & & & & & & & & & & & & =11:8&& & & & &答：小刚和小丽的速度比为11：8& & & & & & & & & & & & & & & & & & & & & & & & & & && 追问： 10/6怎么算出来的 回答： 甲数与乙数的比是9比4,甲数比乙数多()%解：（9-4）÷4=125%答：甲数比乙数多(125)% 补充： 10/6怎么算出来的？答：长方形的长为： &2÷（1+5）X5=10/6=5/3& &2÷（1+5）X5& =2÷6X5& =2X5÷6& =10÷6& =10：6& =10/6 补充： 甲数是乙数的1又5分之3,乙数与甲数的比是?解：因为甲数是乙数的1又5分之3；& &所以，甲数：乙数=1又5分之3& & & & & & & & & & & & & & & &=1+3/5& & & & & & & & & & & & & & & &=5/5+3/5& & & & & & & & & & & & & & & &=8/5& & & & & & & & & & & & & & & &=8:5& & 所以，乙数：甲数=5：8答：乙数与甲数的比是5：8 补充： a.b都是不等于0的自然数,如果a*7=b*9,那么a:b=():()解：因为a*7=b*9& & & 则等式两边同时除以b，得：& & & & & a*7÷b=9& & &等式两边同时除以7，得：& & & & &a÷b=9÷7& & &即 a:b=9:7答：那么a:b=(9):(7) 补充： 朋友，你的题目，我已经帮你解答。。答案是对的。。如果觉得我的解答对你有帮助的话。。希望能采纳支持我一下。。谢谢。。如有不明白的地方。。请追问。。谢谢。。 补充： 10/6怎么算出来的？答：长方形的长为： &2÷（1+5）X5=10/6=5/3& &2÷（1+5）X5& =2÷6X5& =2X5÷6& =10÷6& =10：6& =10/6现在看懂了没有。。如果没有看懂。。请追问。。如果看懂了。。望采纳。。谢谢。。 解决方案2： 5分之4:0.25化成最简整数比是(),比值是小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。甲数与乙数的比是9比4,甲数比乙数多()%甲数是乙数的1又5分之3,乙数与甲数的比是a.b都是不等于0的自然数,如果a*7=b* 补充： 5分之4:0.25化成最简整数比是(16:5),比值是3.2小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。8:11甲数与乙数的比是9比4,甲数比乙数多(125)%甲数是乙数的1又5分之3,乙数与甲数的比是:5:8a.b都是不等于0的自然数,如果a*7=b*（这个是什么）请追问。 补充： b后面乘以什么啊？ 补充： 答案正确，盼亲采纳答案，非常感谢。 追问： a.b都是不等于0的自然数,如果a*7=b*9,那么a:b=():() 回答： a.b都是不等于0的自然数,如果a*7=b*9,那么a:b=(9):(7) 补充： 看懂了吗？如果没有，请追问。 追问： 5分之4:0.25化成最简整数比是(16:5),比值是3.2我好像看不懂 追问： 小刚行走的路程比小丽多四分之一，而小丽走路所用的时间比小刚多十分之一，小刚和小丽的速度比是多少。8:11我也看不懂 追问： 甲数与乙数的比是9比4,甲数比乙数多(125)%不懂
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京ICP备号-1 京公网安备02号12.25-3.1+0.75-6.9,3.75×1.8+2.25×1.8,2.5×1.25×32,[（9+0.25）×12]÷30,12.5×[（0.72-0.16）÷7],3.85×101-3.85,17.8-5.8-1.68÷0.4,56.9-16.2×39.5×0-17.9．，
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延伸：本文除了聚合《12.25-3.1+0.75-6.9,3.75×1.8+2.25×1.8,2.5×1.25×32,[（9+0.25）×12]÷30,12.5×[（0.72-0.16）÷7],3.85×101-3.85,17.8-5.8-1.68÷0.4,56.9-16.2×39.5×0-17.9．》，免费提供的有关3.75双色led显示屏和的内容之一，已有不少的网友认为此答案对自己有帮助！获取更多与《》相关的知识。
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回答问题赢iPhone 6简便：1、【0.25÷（二十分之一+0.2）-二十分之十一×3.82 2、二又五分之二×（六分之五+四分之三）+五分3、 4.8×2又2分之1+6.2×2又2分之1-3×2又2分之1
4、（7.08×5÷7又25分之2×0.24）÷0.5
5、（19.62×3分之1-2.5）÷13分之10
6、（3又3分之1-1.6）×2.5-5分之2×2.5
7、3又3分之2×6+3又3分之2÷2又9分之7
8、9分之43-5.23+9分之74-4.77
9、4分之3÷3分之4×（3.2-1.88）
10、3.87÷4分之5+6.13×5分之4
11、（3又3分之1+0.75-2又8分之5）×1又5分之1
12、9.1÷5分之4-0.9×1又4分之1能做几题就几题。
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99.9*7+11.1*27=11.1×9×7+11.1×27=11.1×（63+27）=11.1×90=999 0.5/0.25+0.95/0.25 =2+3.8=5.84.25/2.5*（10-0.1）+0.17=1.7×9.9+0.17=0.17×99+0.17弗甫缔晃郫浩惦彤定廓=0.17×（99+1）=0.17×100=17
小雁塔小学 &
可以简便的简便计算；99.9*7+11.1*27 解，得：==33.3*27+11.1*27==(33.3+11.1)*27==44.4*27==1198.80.5/0.25+0.95/0.25解，得：==（0.5+0.95）*1/0.25==（0.5+0.95）*4==2+3.8==5.84.25/2.5*（10-0.1）+0.17解，得：==1.7*10-0.1*1.7+0.17==17-0.17+0.17==17
wangku2013&
99.9*7 + 11.1*27= 99.9*7 + 11.1*9*3= 99.9*(7+3)= 99.9*10= 9990.5/0.25 + 0.95/0.25= (0.5 + 0.95) / 0.25= 1.45 / 0.25= (1.45*4) / (0.25*4)= 5.8 / 1= 5.84.25/2.5 * (10-0.1) + 0.17= (4.25*4)/(2.5*4) * (10-0.1) + 0.17= 17/10 * (10-0.1) + 0.17= 17/10 * 10 - 17/10 * 0.1 + 0.17= 17 - 0.17 + 0.17= 17
99.9*7+11.1*27=99.9*7+99.9*3=99.9*（7+3）=99.9*10=999 0.5/0.25+0.95/0.25=（0.5+0.95）/0.25=1.45/0.25=5.8 4.25/2.5*（10-0.1）+0.17=4.25/2.5*10-4.25/2.5*0.1+0.17=1.7*10-1.7*0.1+0.17=17-0.17+0.17=17
99.9*7+11.1*27=99.9*7+99.9*3=99.9*（7+3）=999 0.5/0.25+0.95/0.25 =（0.5+0.95）/0.25=5.84.25/2.5*（10-0.1）+0.17=1.7*9.9+0.17=0.17*99+0.17=0.17*(99+1)=17
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