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Question
At what temperature will the speed of sound in the air be 1.75 times its speed at S.T.P?
Solution
Given:
vair = 1.75 `"V"_"S.T.P." = 7/4 "V"_"STP", "T"_"S.T.P." = 273`K
To find: temperature Tair
Formula: `"v" prop sqrt"T"`
Calculation: From formula,
`"v"_"STP"/"v"_"air" = sqrt(("T"_"STP")/("T"_"air"))`
∴ `"v"_"STP"/(1.75 "v"_"air") = sqrt(273/"T"_"air")`
∴ `"v"_"STP"/(7//4 "v"_"STP") = sqrt((273)/("T"_"air"))`
∴ `"T"_"air" = (273 xx 49)/16`
∴ `"T"_"air"` = 836 K = 563°C
At 836 K (563°C), the speed of sound in air will be 1.75 times its speed at S.T.P.
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