prove speed of sound in air v=331+0.6Tc^° ((m/(sec)))


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Question Number 165072 by mathls last updated on 25/Jan/22

$p r o v e s p e e d o f s o u n d i n a i r$ $v = 331 + 0.6 {T c}^{°} (\frac{m}{s e c})$
Commented by mr W last updated on 25/Jan/22

$c a n y o u p r o v e t h a t t h e S u n i s l a r g e r$ $t h a n t h e M o o n ? c a n y o u p r o v e t h a t$ $a y e a r h a s 365 d a y s ?$ $t h e s e a r e f a c t s . f a c t s c a n n o t b e p r o v e d$ $a n d {n e e d n}^{'} t t o b e p r o v e d .$ $t h e s p e e d o f s o u n d i n t h e a i r i s a l s o$ $a f a c t . t h e s p e e d i n a i r i s n o t a c o n s t a n t,$ $t h i s i s a l s o a f a c t . i t d e p e n d s o n m a n y$ $m a n y f a c t o r s, e . g . t h e t e m p e r a t u r e,$ $t h e p r e s s u r e, t h e r e l a t i v e h u m i d i t y,$ $t h e p o l u t i o n, a n d a n d a n d . t h e s p e e d s$ $o f s o u n d i n a i r a r e f a c t s, t h e v a l u e s$ $a r e m e a s u r e d, n o t c a l c u l a t e d! t h e$ $d e p e n d e n c e o f m e a s u r e d s o u n d s p e e d o n t h e$ $t h e t e m p e r a t u r e c a n b e a p p r o x i m a t e l y$ $d e s c r i b e d w i t h v = 331 + 0.6 T . b u t t h i s$ $i s n o t a m a t h e m a t i c a l o r p h y s i c a l$ $t h e o r e m w h i c h y o u c a n p r o v e o r y o u$ $c a n d e r i v a t e . {i t}^{'} s j u s t a a p p r o x i m a t i o n$ $o f f a c t s .$ $o t h e r p e o p l e d e s c r i b e t h e s a m e$ $d e p e n d e n c e w i t h v = 20.05 \sqrt{273.16 + T} .$ $t h i s i s a l s o o n l y a n a p p r o x i m a t i o n .$ $m a y b e y o u c a n f i n d e v e n a b e t t e r$ $a p p r o x i m a t i o n i n f o r m o f$ $v = {a T}^{2} + b T + c \sqrt[3]{T} + d \ln α T .$
Commented by mr W last updated on 25/Jan/22

$a s i h a v e s a i d t h e f o r u m i s n o t a$ $g o o d p l a c e f o r y o u t o l e a r n f a c t s o r$ $e l e m e n t a r y t h i n g s . g o t o o t h e r p l a c e s$ $l i k e g o o g l e!$
Commented by mathls last updated on 25/Jan/22

$m y m a i n p u r p o s e i s i t t o p r o v e t h e$ $a p p r o x i m a t i o n (v = 331 + 0.6 {T c}^{°})$
Commented by mr W last updated on 25/Jan/22

$y o u c a n n o t p r o v e a n a p p r o x i m a t i o n!$ $a s i h a v e s a i d, y o u c a n e v e n c o n s t r u c t$ $a n a p p r o x i m a t i o n o f y o u r o w n f o r$ $t h e s a m e d a t a .$ $g o t o g o o g l e a n d s e a r c h ‘ ‘ h o w t o f i n d$ $c u r v e o f b e s t {f i t}^{″} .$
Commented by mathls last updated on 25/Jan/22

$n o t i s i n t h e g o o g l e b u t h o w w e c a n$ $f i n d t h a t ?$
Commented by mathls last updated on 26/Jan/22

$h o w w e c a n f i n d t h i s a p p r o x i m a t i o n ?$
Commented by mr W last updated on 26/Jan/22

$g o t o g o o g l e a n d t y p e ‘ ‘ s o u n d s p e e d i n$ ${a i r}^{″} a n d t h e n j u s t r e a d, r e a d, r e a d . . .$
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

$w h e n i c a n f i n d, w h y c a n y o u n o t f i n d ?$ $w h e r e a r e y o u f r o m ? i s g o o g l e$ $r e s t r i c t e d i n y o u r c o u n t r y ?$
Commented by Tinku Tara last updated on 26/Jan/22

$For theory question such as this you$ $will find google search gives good$ $answers . For maths problems$ $google search will not give good results .$
Commented by mathls last updated on 26/Jan/22

$h o w w e c a n g e t 331.3 \sqrt{1 + \frac{ϑ}{273.15}} f r o m$ $v = \sqrt{\frac{γ R T}{M}} ? p l e a s e d e s c r i b e t h e i u n d e r s t a n d .$
Commented by mathls last updated on 26/Jan/22

$h o w w e c a n s i m p l i f y f r o m r o o t ?$ $\sqrt{1 + \frac{ϑ}{273.15}} ?$
Commented by mr W last updated on 26/Jan/22

$h a v e y o u r e a d t h e a r t i c l e i n$ $w i k i p e d i a ?$ $A) n o, y o u {h a v n}^{'} t .$ $\Rightarrow t h e n y o u a r e t o o l a z y . s i n c e i {d o n}^{'} t$ $l i k e t o l o s e m y t i m e f o r l a z y p e o p l e,$ $i {w o n}^{'} t s a y a n y t h i n g m o r e .$ $B) y e s, y o u h a v e, b u t y o u s t i l l {d o n}^{'} t$ $u n d e r s t a n d t h e c o n t e n t t h e r e .$ $\Rightarrow t h e n t h e t h i n g i s t o o h i g h f o r y o u r$ $l e v e l a t t h e m o m e n t . i f y o u e v e n {d o n}^{'} t$ $u n d e r s t a n d t h e e x p l a n a t i o n i n t h e$ $a r t i c l e, w h i c h i s v e r y d e t a i l e d a n d$ $c o m p r e h e n s i v e, t h e n i c a n a l s o n o t$ $h e l p y o u f u r t h e r, b e c a u s e i {c a n}^{'} t$ $e x p l a i n i t b e t t e r t h a n t h e a r t i c l e .$ $m y s u g g e s t i o n i s t h a t y o u l e t t h e t h i n g$ $b e a n d w a i t s o m e t i m e t i l l y o u h a v e$ $l e a r n t a l i t t l e m o r e i n p h y s i c s a n d$ $m a t h e m a t i c s, f o r e x a m p l e w h a t i s$ $a b s o l u t e t e m p e r a t u r e a n d w h a t i s$ $t a y l o r e x p a n s i o n o f a f u n c t i o n e t c .$
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