Solution
Given,
Frequency of sound (f) = 512 Hz
The wavelength of sound (λ) = 66.5 cm = 0.665 m
Temperature (T) = 17°C = 17 + 273 K = 290 K
Ratio of molar heat capacities (γ) = ?
Now,
\(\frac{v_0}{v_{17}}=\sqrt{\frac{T_0}{T_{17}}}=\sqrt{\frac{273}{290}}=0.97\)
Or, v0 = 0.97 x 340.48 = 330.26 m/s
Now, velocity of sound in air is given by,
\(v_0=\sqrt{\frac{\gamma P}\rho}\)
Or, \(v_0=\sqrt{\frac{\gamma\rho_mgh}{\rho_a}}\)
Or, \(330.26=\sqrt{\frac{\gamma\times13600\times10\times0.76}{1.29}}\)
Or, \(330.26=\sqrt{\gamma\times80124.03}\)
Or, \(330.26^2=\gamma\times80124.03\)
Or, γ = 1.36
Hence, the molar heat capacities at constant pressure to constant volume at NTP is 1.36
