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 = v_o ?(T/T_o)

where v_o is the velocity of sound at temperatureT_o.

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 ofv_o and T_o?

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

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

genius_generous answered 2 years ago

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