Question

The velocity of sound in dry air at $0^{\circ }C$ and at 74 cm of Hg pressure is 332 $m{s}^{-1}$ Then the velocity of sound (in $m{s}^{-1}$ ) at ${50}^{\circ }C$ and 77.5 cm of Hg pressure will be

• A. $322.7$
• B. $347.1$
• C. $352.4$
• D. $361.1$

Answer 1

The correct option is D $361.1$

Velocity of sound waves in ideal gases do not depend on pressure or density. It depends only on temperature

$v=\sqrt{\frac{rRT}{M}=\sqrt{rP}\rho }$

Velocity of sound at $0^o$C and $74$ mm Hg pressure $=332$m/s

Velocity of sound at ${50}^o$C and $77.5$ mm Hg pressure $=?$

As we know,

Velocity of sound in air is proportional to square root of absolute temperature

$v\propto \sqrt{T}$, where T$=$ absolute temperature

$\frac{vat{50}^{o}C}{vat{0}^{o}C}=\frac{\sqrt{273.15+50}}{\sqrt{273.15}}$

v at ${50}^o$C $=361.11$ m/s.