The speed of sound in air at NTP is 332 ms$^{-1}$. Calculate the percentage error in speed of sound as…
The speed of sound in air at NTP is 332 ms$^{-1}$. Calculate the percentage error in speed of sound as calculated from Newton's formula. Given that the density of air at 1 atm pressure is 1.293 kgm$^{-3}$.
Solution
Sol. From Newton's formula, $v=\sqrt{p/\rho}$
At NTP, $p=1.01\times10^5\ \mathrm{Pa}\ \Rightarrow\ v=\sqrt{\dfrac{1.01\times10^5}{1.293}}=280\ \mathrm{ms}^{-1}$
Difference in speed $=332-280=52\ \mathrm{ms}^{-1}$
$\%\ \text{error}=\dfrac{52}{332}\times100=15.7\%$
Answer: $15.7\%$