Question

at what temperature will the speed of sound in air be 1.75 times its speed at NTP​

Answer 1

Answer:

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Answer 2

Answer:

897.77 K

Explanation:

Speed of sound

$c=\sqrt{\gamma R_* T_1}$

Where,

$\gamma$ = Adiabatic index

$R_*$ = Mass-specific gas constant

$T_1$ = Temperature = 273.15+20 = 293.15 K

$1.75c=\sqrt{\gamma R_* T_2}$

Dividing the equations we get

$\frac{1.75c}{c}=\frac{\sqrt{\gamma R_* T_2}}{\sqrt{\gamma R_* T_1}}\\\Rightarrow 1.75=\sqrt{\frac{T_2}{T_1}}\\\Rightarrow 1.75^2=\frac{T_2}{T_1}\\\Rightarrow 1.75^2=\frac{T_2}{293.15}\\\Rightarrow T_2=1.75^2\times 293.15\\\Rightarrow T_2=897.77\ K$

The temperature of air would be 897.77 K