Speed of Sound (warm air or cold air)

AI Thread Summary
Sound travels faster in warm air than in cold air due to the relationship between temperature and molecular motion, as described by the equation v = 331 + (0.59Tc). While denser mediums can transmit sound more effectively, the density of cold air does not compensate for the increased speed associated with higher temperatures. At night, sound is often clearer over water because of reduced background noise rather than an increase in the speed of sound. The speed of sound is influenced by temperature, as warmer air allows air particles to move more freely, enhancing sound wave propagation. Therefore, the clarity of sound at night is primarily due to lower noise levels, not an increase in speed.
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I am so confused with speed of sound. would sound travel faster in cold or warm air?
if you put mathmatical equation in, v= 331 + (0.59Tc) then it would travel faster in warm air.
but another theory says that sound travels faster in denser medium and cold air is denser than warm air, hence it travels faster in colder air. it it true?

And at night over water we can hear sound clearly on shore than during the day because of colder air during night and over water, as cold air is dense, molecules can bump into each other better as they are closer, makes it travel faster? or the speed of it has nothing to do with it? would the answer be just (it travels better because it is denser)?

please help me out thanks
 
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More likely at night over water, there is less background noise, so one can hear more clearly, but the speed of sound is not increased.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe.html
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe3.html

The speed of sound (in a gas) is inversely proportional to M1/2, where M is the molecular (or atomic mass for monatomic (noble) gases), and that of course is related to density. On the other hand, the speed of sound increases with temperature even as density decreases slightly.
 
Astronuc said:
More likely at night over water, there is less background noise, so one can hear more clearly, but the speed of sound is not increased.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe.html
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe3.html

The speed of sound (in a gas) is inversely proportional to M1/2, where M is the molecular (or atomic mass for monatomic (noble) gases), and that of course is related to density. On the other hand, the speed of sound increases with temperature even as density decreases slightly.

yes but if you were to explain using physics how would you explain that at night over water u can hear sound clearly than during the day?
 
As temperature increases, air particles move more, and allow for better propagation of sound waves
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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