In: Physics
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?
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