Question

A pulse of sound wave travels a distance $l$ in helium gas in time $T$ at a particular temperature. If at the same temperature a pulse of sound wave is propagated in oxygen gas, it will cover the same distance $l$ in time.

• A. $4.36T$
• B. $0.23T$
• C. $3T$
• D. $0.46T$

Answer 1

The correct option is C $3T$

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

$\Rightarrow v_1=\sqrt{\frac{5}{3}\frac{RT}{4}}$

$\Rightarrow v_2=\sqrt{\frac{7}{5}\frac{RT}{32}}$

$\Rightarrow T=l\sqrt{\frac{3\times 4}{5RT}}$

$\Rightarrow T^1=l\sqrt{\frac{5\times 32}{7RT}}$

$\Rightarrow \frac{T^1}{T}=\sqrt{\frac{5\times 32}{7}}\sqrt{\frac{5}{3\times 4}}$

$=\frac{5\times 2\sqrt{2}}{\sqrt{21}}$

$=3.08\approx 3$

$\Rightarrow T^1=3T$