Question

At what temperature will the speed of sound in air be 1.75 times its speed at N.T.P?

Answer 1

Given:
v_air = 1.75 `"V"_"N.T.P." = 7/4 "V"_"NTP", "T"_"N.T.P." = 293`K

To find: temperature T_air

Formula: `"v" prop sqrt"T"`

Calculation: From formula,

`"v"_"NTP"/"v"_"air" = sqrt(("T"_"NTP")/("T"_"air"))`

∴ `"v"_"NTP"/(1.75 "v"_"air") = sqrt(293/"T"_"air")`

∴ `"v"_"NTP"/(7//4 "v"_"STP") = sqrt((293)/("T"_"air"))`

∴ `"T"_"air" = (293 xx 49)/16`

∴ `"T"_"air"` = 897 K = 624°C

At 897 K (624°C), the speed of sound in air will be 1.75 times its speed at N.T.P.