Question: In this problem, you will derive a convenient formula for the speed of sound in air at temperature t in Celsius degrees. Begin by writing

In this problem, you will derive a convenient formula for the speed of sound in air at temperature t in Celsius degrees. Begin by writing the temperature as T = T₀ + ∆T, where T₀ = 273 K corresponds to 0^oC and ∆T = t, the Celsius temperature. The speed of sound is a function of T, v(T). To a first-order approximation, you can write

v(T) ≈ v(T₀) + (dv/dT ) _T0 ∆T,

where (dv/dT)_T₀ is the derivative evaluated at T = T₀. Compute this derivative, and show that the result leads to

' = (331 m/s)| 1+ 27 (331+0.6061)m/s

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