SATHEE: Wave Motion 3 Question 7

Wave Motion 3 Question 7

7. The ratio of the velocity of sound in hydrogen gas $(γ = \frac{7}{5})$ to that in helium gas $(γ = \frac{5}{3})$ at the same temperature is

$\sqrt{21 / 5}$ .

(1983, 2M)

Show Answer

Answer:

Correct Answer: 7. $F$

Solution:

$v_{sound} = \sqrt{\frac{γ R T}{M}} \Rightarrow \frac{v_{H_{2}}}{v_{H e}} = \frac{\sqrt{γ_{H_{2}} / M_{H_{2}}}}{\sqrt{γ_{H e} / M_{H e}}} = \frac{\sqrt{(7 / 5) / 2}}{\sqrt{(5 / 3) / 4}} = \sqrt{\frac{42}{25}}$

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