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May 1st, 2012, 08:37 PM   #1
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Rate of changes

Think this goes in this forum

Speed of sound in air at 0 degrees celsius (or 273 kelvins) is 331.5m/s but speed v increases as the temperature T rises.
we know that the rate of change of v in respect to T is

(dv/dT) = (331.5) / (2 sqrt(273T)

where v is metres and T kelvins. find a formula that expresses v as a function of the temperature (T)


how would i do this? thanks
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May 1st, 2012, 10:01 PM   #2
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Math Focus: Calculus/ODEs
Re: Rate of changes

We are given the initial value problem:

where and .

Write the ordinary differential equation as:



Now integrate:





And we find the general solution:



Now, we need to use the initial value to determine the constant of integration, or parameter:







And so, the solution satisfying the given condition is:

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