Question

For air at room temperature the atmospheric pressure is $1.0\times {10}^5$ $N{m}^{-2}$ and density of air is $1.2kg$ $m^{-3}$. For tube of length $1.0m$ closed at one end the lowest frequency generated is $84Hz$. The value of $\gamma$ (ratio of two specific heats) for air is:

• A. $2.1$
• B. $1.5$
• C. $1.8$
• D. $1.4$

Answer 1

The correct option is D $1.4$

For tube closed at one end, fundamental frequency is given by:

$f=\frac{v}{4l}$

According to newton's formula, speed of sound in a medium is given by:

$v=\sqrt{\frac{\gamma P}{\rho }}$

Equating speed from above two equations, we get:

$\sqrt{\frac{\gamma P}{\rho }}=4fl$

$\gamma =\frac{(4fl{)}^2\rho }{P}$

$⟹\gamma =\frac{(84\times 4{)}^2\times 1.2}{1.0\times {10}^5}=1.354\approx 1.4$