•.• Derive a convenient formula for the speed of sound in air at temperature t in degrees Celsius. Begin by writing the tempera- ture as T = T, + AT, where T, AT = t, which is 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(T,) + (dv/dT), AT, where (dv/dT),, is the derivative eval- uated at T = T. Compute this derivative, and show that the result leads to 35 273 K and corresponds to 0°C and (331 m/s)(1 + (t/2T,)) = (331 + 0.606t) m/s V =
•.• Derive a convenient formula for the speed of sound in air at temperature t in degrees Celsius. Begin by writing the tempera- ture as T = T, + AT, where T, AT = t, which is 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(T,) + (dv/dT), AT, where (dv/dT),, is the derivative eval- uated at T = T. Compute this derivative, and show that the result leads to 35 273 K and corresponds to 0°C and (331 m/s)(1 + (t/2T,)) = (331 + 0.606t) m/s V =
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Transcribed Image Text:•.• Derive a convenient formula for the speed of sound in air
at temperature t in degrees Celsius. Begin by writing the tempera-
ture as T = T, + AT, where T, = 273 K and corresponds to 0°C and
AT = t, which is 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(T,) + (dv/dT),, AT, where (dv/dT),, is the derivative eval-
uated at T = T: Compute this derivative, and show that the result
leads to
35
V
v = (331 m/s)(1 + (t/2T,)) = (331 + 0.606t) m/s
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