Hi everyone ,
I just remembered what my 9th Grade text book said .
Sound travels faster in higher temperatures.
It also mentions that as the Density increase , the speed also increases.
If density increases , the temperature decreases and vice-versa . Now These statements contradict each other ??? .
Does anyone know what the actual relation of Sound , Density and Temperature is ? (Please correct me if the above statements are wrong)
Thankyou :)
Well, to answer your question, as far as I know for different gases the speed of sound is inversely proportional to density. Because according to Laplace's formula, speed of sound = [Y P/D]^1/2,i.e Sqrt of Gamma X Pressure divided by density of the medium. So, it increases when density decreases.
But for the same gas the speed of sound is independent of density.
It has nothing to do with density or pressure it is only dependent on temperature in fact the formula is :-
Speed of Sound (In Knots) = 39 √t where t is temp absolute (i.e in kelvin) 39 is a constant
Example 1 (At Sea Level)
As per International Standard Atmosphere, surface temperature is 15° C i.e 288° Kelvin
that Makes speed of sound at Sea Level is 663 Knots (Nautical Miles an Hour).
Example 2 (At 40,000 Feet)
As per International Standard Atmosphere, temperature drop for every 1000 feet is 1.98°. Therefore at 40,000 temperature drop from Sea Level Would be 79° from +15° the actual OAT (Outside Air Temp) will be (79-15) -64°. At this temp what would be the speed of sound ? it would be 39√209 = 565 Knots
But gusty bhaiya for different gases it is inversely proportional to density, i.e if i keep two different gases at the same temperature, then the speed of the sound will be more in the one that has lesser density.
Could you explain it in a simpler way ?
I still haven't learnt about what all your talking ???
Speed of sound is basically square root of ratio of bulk modulus and density of material.
Now if we look at ideal gas equation then we can convert the speed of sound in ideal gas to square root of ratio of (gammaxRxT) and molar mass. So for particular ideal gas sound varies with square root of temperature only. In case of solids and liquids things go in little different way as idea gas equation is not valid but above said basic formula is same for all.
You need to know that the fundamental equation for any sound wave says that, speed of any longitudinal wave(including sound wave) is directly proportional to the elasticity of the medium and inversely proportional to the density of the medium.
Now, when you are talking of substances which are solid in nature, their elasticity is more then that of Liquids and Gases because the atoms in solids are tightly packed and compact whereas in liquids and gases there is a certain amount of random motion in them. This is why the speed of sound is more in Solids than in liquids and gases and that is why you got the misconception that since the density of solids is more than that of fluids(in general), hence the speed of sound should increase with the increase in density, this is wrong.
Alright now come to fluids lets take gases. In the case of gases there is a little correction to the formula for the speed of sound, here the formula is proportional to pressure and inversely proportional to density. Now, the case here is that pressure and density are themselves interrelated so the statement i have made just before this is not completely true. If u use the ideal gas equation i.e, PV=nRT and with some deductions you will end with a formula which says that the speed is proportional to sqrt of temp divided by the mass(Molecular or atomic mass if you consider 1 mole of the substance).
So, according to this velocity of sound for a particular gas depends only on the temperature since the molecular mass is constant. But if I consider two different gases at the same temperature, then the one with the higher density will have greater molecular mass and hence leading to a lower speed of sound in that gas.
Now, read this twice over and take your time.
If you want to go in more details then refer to this http://en.wikipedia.org/wiki/Speed_of_sound (http://en.wikipedia.org/wiki/Speed_of_sound)