Question

In: Physics

The velocity of sound, v (m/s), increases as the square rootof the absolute temperature, T (K):...

The velocity of sound, v (m/s), increases as the square rootof the absolute temperature, T (K):

   v = vo ?(T/To)

where vo is the velocity of sound at temperatureTo.

a) Make a rough sketch of how the graph of v versus T wouldlook.

b) If one measures v for several temperatures, T, how couldyou plot the data so as to get a straight line?

c) What would be the slope of this straight line, in terms ofvo and To?

d) What would be the SI units of this slope?

Solutions

Expert Solution

a) v = v0/?T0 * ?T = a ?T.where a = v0/?T0


b) ln(v) = ln(a) + (1/2) ln(T)
so ln(v) ~ ln(T) is a straight line
c) slope is 1/2
d) slope 1/2 has no units


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