Speed as func. of distance

1. May 30, 2010

aim1732

Q:The absolute temperature of air in a region linearly increases from T1 to T2 in a space of width d. Find time taken by sound wave to go through the region in terms of T1 T2,d and speed v of sound at 273K.

Equations :

vt = v( 1 + t/546)
dt = dx/v

Attempt:
I was basically looking to express speed of sound as a function of distance and integrating.

Assuming linear increase in temperature with distance
T(general) = T1 + [T2-T1]*x/d

Therefore
v(general) = v[ 1 + (T1 + [T2-T1]*x/d)/546 ]

dt = dx/v
= 546d (dx)/ v( 546d +T1d + {T2 -T1}x )

Am I right with this? I was hoping for an easier way as I am not sure if this is correct.

2. Jun 1, 2010

Coto

I'm a little confused on what you are trying to do.

What is your $$v_t$$ formula? Does $$t$$ represent temperature for this formula? What is $$v$$?

3. Jun 1, 2010

aim1732

Actually v is velocity and t is temperature so vt is velocity at that temperature.

vt/v273 = sqrt(T/273)
t=T+273 and using binomial expansion we have the result.