Wave Motion 3 Question 7
7. The ratio of the velocity of sound in hydrogen gas $\left(\gamma=\frac{7}{5}\right)$ to that in helium gas $\left(\gamma=\frac{5}{3}\right)$ at the same temperature is
$\sqrt{21 / 5}$.
(1983, 2M)
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Answer:
Correct Answer: 7. $F$
Solution:
- $v _{\text {sound }}=\sqrt{\frac{\gamma R T}{M}} \Rightarrow \frac{v _{H _2}}{v _{He}}=\frac{\sqrt{\gamma _{H _2} / M _{H _2}}}{\sqrt{\gamma _{He} / M _{He}}}=\frac{\sqrt{(7 / 5) / 2}}{\sqrt{(5 / 3) / 4}}=\sqrt{\frac{42}{25}}$
