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Speed as func. of distance

  1. May 30, 2010 #1
    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. jcsd
  3. Jun 1, 2010 #2
    I'm a little confused on what you are trying to do.

    What is your [tex]v_t[/tex] formula? Does [tex]t[/tex] represent temperature for this formula? What is [tex]v[/tex]?
     
  4. Jun 1, 2010 #3
    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.
     
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