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prove-speed-of-sound-in-air-v-331-0-6Tc-m-sec-




Question Number 165072 by mathls last updated on 25/Jan/22
prove speed of sound in air  v=331+0.6Tc^° ((m/(sec)))
$${prove}\:{speed}\:{of}\:{sound}\:{in}\:{air} \\ $$$${v}=\mathrm{331}+\mathrm{0}.\mathrm{6}{Tc}^{°} \left(\frac{{m}}{{sec}}\right) \\ $$
Commented by mr W last updated on 25/Jan/22
can you prove that the Sun is larger  than the Moon? can you prove that  a year has 365 days?  these are facts. facts can not be proved  and needn′t to be proved.  the speed of sound in the air is also  a fact. the speed in air is not a constant,  this is also a fact. it depends on many  many factors, e.g. the temperature,  the pressure, the relative humidity,  the polution, and and and. the speeds  of sound in air are facts, the values  are measured, not calculated! the  dependence of measured sound speed on the  the temperature can be approximately  described with v=331+0.6T. but this  is not a mathematical or physical  theorem which you can prove or you  can derivate. it′s just a approximation   of facts.  other people describe the same  dependence with v=20.05(√(273.16+T)).  this is also only an approximation.  maybe you can find even a better  approximation in form of  v=aT^2 +bT+c(T)^(1/3) +d ln αT.
$${can}\:{you}\:{prove}\:{that}\:{the}\:{Sun}\:{is}\:{larger} \\ $$$${than}\:{the}\:{Moon}?\:{can}\:{you}\:{prove}\:{that} \\ $$$${a}\:{year}\:{has}\:\mathrm{365}\:{days}? \\ $$$${these}\:{are}\:{facts}.\:{facts}\:{can}\:{not}\:{be}\:{proved} \\ $$$${and}\:{needn}'{t}\:{to}\:{be}\:{proved}. \\ $$$${the}\:{speed}\:{of}\:{sound}\:{in}\:{the}\:{air}\:{is}\:{also} \\ $$$${a}\:{fact}.\:{the}\:{speed}\:{in}\:{air}\:{is}\:{not}\:{a}\:{constant}, \\ $$$${this}\:{is}\:{also}\:{a}\:{fact}.\:{it}\:{depends}\:{on}\:{many} \\ $$$${many}\:{factors},\:{e}.{g}.\:{the}\:{temperature}, \\ $$$${the}\:{pressure},\:{the}\:{relative}\:{humidity}, \\ $$$${the}\:{polution},\:{and}\:{and}\:{and}.\:{the}\:{speeds} \\ $$$${of}\:{sound}\:{in}\:{air}\:{are}\:{facts},\:{the}\:{values} \\ $$$${are}\:{measured},\:{not}\:{calculated}!\:{the} \\ $$$${dependence}\:{of}\:{measured}\:{sound}\:{speed}\:{on}\:{the} \\ $$$${the}\:{temperature}\:{can}\:{be}\:{approximately} \\ $$$${described}\:{with}\:{v}=\mathrm{331}+\mathrm{0}.\mathrm{6}{T}.\:{but}\:{this} \\ $$$${is}\:{not}\:{a}\:{mathematical}\:{or}\:{physical} \\ $$$${theorem}\:{which}\:{you}\:{can}\:{prove}\:{or}\:{you} \\ $$$${can}\:{derivate}.\:{it}'{s}\:{just}\:{a}\:{approximation}\: \\ $$$${of}\:{facts}. \\ $$$${other}\:{people}\:{describe}\:{the}\:{same} \\ $$$${dependence}\:{with}\:{v}=\mathrm{20}.\mathrm{05}\sqrt{\mathrm{273}.\mathrm{16}+{T}}. \\ $$$${this}\:{is}\:{also}\:{only}\:{an}\:{approximation}. \\ $$$${maybe}\:{you}\:{can}\:{find}\:{even}\:{a}\:{better} \\ $$$${approximation}\:{in}\:{form}\:{of} \\ $$$${v}={aT}^{\mathrm{2}} +{bT}+{c}\sqrt[{\mathrm{3}}]{{T}}+{d}\:\mathrm{ln}\:\alpha{T}. \\ $$
Commented by mr W last updated on 25/Jan/22
as i have said the forum is not a  good place for you to learn facts or  elementary things. go to other places  like google!
$${as}\:{i}\:{have}\:{said}\:{the}\:{forum}\:{is}\:{not}\:{a} \\ $$$${good}\:{place}\:{for}\:{you}\:{to}\:{learn}\:{facts}\:{or} \\ $$$${elementary}\:{things}.\:{go}\:{to}\:{other}\:{places} \\ $$$${like}\:{google}! \\ $$
Commented by mathls last updated on 25/Jan/22
my main purpose is it to prove the  approximation(v=331+0.6Tc^° )
$${my}\:{main}\:{purpose}\:{is}\:{it}\:{to}\:{prove}\:{the} \\ $$$${approximation}\left({v}=\mathrm{331}+\mathrm{0}.\mathrm{6}{Tc}^{°} \right) \\ $$
Commented by mr W last updated on 25/Jan/22
you can not prove an approximation!  as i have said, you can even construct   an approximation of your own for   the same data.  go to google and search “how to find  curve of best fit”.
$${you}\:{can}\:{not}\:{prove}\:{an}\:{approximation}! \\ $$$${as}\:{i}\:{have}\:{said},\:{you}\:{can}\:{even}\:{construct}\: \\ $$$${an}\:{approximation}\:{of}\:{your}\:{own}\:{for}\: \\ $$$${the}\:{same}\:{data}. \\ $$$${go}\:{to}\:{google}\:{and}\:{search}\:“{how}\:{to}\:{find} \\ $$$${curve}\:{of}\:{best}\:{fit}''. \\ $$
Commented by mathls last updated on 25/Jan/22
not is in the google but how we can  find that?
$${not}\:{is}\:{in}\:{the}\:{google}\:{but}\:{how}\:{we}\:{can} \\ $$$${find}\:{that}? \\ $$
Commented by mathls last updated on 26/Jan/22
how we can find this approximation?
$${how}\:{we}\:{can}\:{find}\:{this}\:{approximation}? \\ $$
Commented by mr W last updated on 26/Jan/22
go to google and type “sound speed in  air” and then just read, read, read ...
$${go}\:{to}\:{google}\:{and}\:{type}\:“{sound}\:{speed}\:{in} \\ $$$${air}''\:{and}\:{then}\:{just}\:{read},\:{read},\:{read}\:… \\ $$
Commented by mr W last updated on 26/Jan/22
Commented by mr W last updated on 26/Jan/22
Commented by mr W last updated on 26/Jan/22
when i can find, why can you not find?  where are you from? is google   restricted in your country?
$${when}\:{i}\:{can}\:{find},\:{why}\:{can}\:{you}\:{not}\:{find}? \\ $$$${where}\:{are}\:{you}\:{from}?\:{is}\:{google}\: \\ $$$${restricted}\:{in}\:{your}\:{country}? \\ $$
Commented by Tinku Tara last updated on 26/Jan/22
For theory question such as this you  will find google search gives good  answers. For maths problems  google search will not give good results.
$$\mathrm{For}\:\mathrm{theory}\:\mathrm{question}\:\mathrm{such}\:\mathrm{as}\:\mathrm{this}\:\mathrm{you} \\ $$$$\mathrm{will}\:\mathrm{find}\:\mathrm{google}\:\mathrm{search}\:\mathrm{gives}\:\mathrm{good} \\ $$$$\mathrm{answers}.\:\mathrm{For}\:\mathrm{maths}\:\mathrm{problems} \\ $$$$\mathrm{google}\:\mathrm{search}\:\mathrm{will}\:\mathrm{not}\:\mathrm{give}\:\mathrm{good}\:\mathrm{results}. \\ $$
Commented by mathls last updated on 26/Jan/22
how we can get 331.3(√(1+(ϑ/(273.15)))) from  v=(√((γRT)/M))  ?  please describe the i understand.
$${how}\:{we}\:{can}\:{get}\:\mathrm{331}.\mathrm{3}\sqrt{\mathrm{1}+\frac{\vartheta}{\mathrm{273}.\mathrm{15}}}\:{from} \\ $$$${v}=\sqrt{\frac{\gamma{RT}}{{M}}}\:\:?\:\:{please}\:{describe}\:{the}\:{i}\:{understand}. \\ $$
Commented by mathls last updated on 26/Jan/22
how we can simplify from root?  (√(1+(ϑ/(273.15))))?
$${how}\:{we}\:{can}\:{simplify}\:{from}\:{root}? \\ $$$$\sqrt{\mathrm{1}+\frac{\vartheta}{\mathrm{273}.\mathrm{15}}}? \\ $$
Commented by mr W last updated on 26/Jan/22
have you read the article in   wikipedia?  A) no, you havn′t.  ⇒ then you are too lazy. since i don′t   like to lose my time for lazy people,   i won′t say anything more.  B) yes, you have, but you still don′t   understand the content there.  ⇒ then the thing is too high for your   level at the moment. if you even don′t  understand the explanation in the  article, which is very detailed and  comprehensive, then i can also not  help you further, because i can′t  explain it better than the article.  my suggestion is that you let the thing  be and wait some time till you have   learnt a little more in physics and   mathematics, for example what is   absolute temperature and what is   taylor expansion of a function etc.
$${have}\:{you}\:{read}\:{the}\:{article}\:{in}\: \\ $$$${wikipedia}? \\ $$$$\left.{A}\right)\:{no},\:{you}\:{havn}'{t}. \\ $$$$\Rightarrow\:{then}\:{you}\:{are}\:{too}\:{lazy}.\:{since}\:{i}\:{don}'{t}\: \\ $$$${like}\:{to}\:{lose}\:{my}\:{time}\:{for}\:{lazy}\:{people},\: \\ $$$${i}\:{won}'{t}\:{say}\:{anything}\:{more}. \\ $$$$\left.{B}\right)\:{yes},\:{you}\:{have},\:{but}\:{you}\:{still}\:{don}'{t}\: \\ $$$${understand}\:{the}\:{content}\:{there}. \\ $$$$\Rightarrow\:{then}\:{the}\:{thing}\:{is}\:{too}\:{high}\:{for}\:{your}\: \\ $$$${level}\:{at}\:{the}\:{moment}.\:{if}\:{you}\:{even}\:{don}'{t} \\ $$$${understand}\:{the}\:{explanation}\:{in}\:{the} \\ $$$${article},\:{which}\:{is}\:{very}\:{detailed}\:{and} \\ $$$${comprehensive},\:{then}\:{i}\:{can}\:{also}\:{not} \\ $$$${help}\:{you}\:{further},\:{because}\:{i}\:{can}'{t} \\ $$$${explain}\:{it}\:{better}\:{than}\:{the}\:{article}. \\ $$$${my}\:{suggestion}\:{is}\:{that}\:{you}\:{let}\:{the}\:{thing} \\ $$$${be}\:{and}\:{wait}\:{some}\:{time}\:{till}\:{you}\:{have}\: \\ $$$${learnt}\:{a}\:{little}\:{more}\:{in}\:{physics}\:{and}\: \\ $$$${mathematics},\:{for}\:{example}\:{what}\:{is}\: \\ $$$${absolute}\:{temperature}\:{and}\:{what}\:{is}\: \\ $$$${taylor}\:{expansion}\:{of}\:{a}\:{function}\:{etc}. \\ $$

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