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Sound travels a distance of 1 m from point P to point Q through a medium in which temperature varies linearly from T0 at P to 4T0 at Q. If the speed of sound in this medium is v = k*sqrt(T) (where k is a constant), how long does the sound wave take to travel this 1 m path?

1. 1/(2k*sqrt(T0))
2. sqrt(T0)/(2k)
3. 2/(3k*sqrt(T0))
4. 3/(2k*sqrt(T0))

Correct answer: 2/(3k*sqrt(T0))

Solution

Substituting u = 1 + 3x and integrating gives t = (2/(3k*sqrt(T0)))*(sqrt(4) - sqrt(1)) = 2/(3k*sqrt(T0)), since the square-root integral evaluates to 2 over the interval from u=1 to u=4.

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