SATHEE: Wave Motion 3 Question 5

Wave Motion 3 Question 5

5. Two monoatomic ideal gases 1 and 2 of molecular masses $m_{1}$ and $m_{2}$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to the gas 2 is given by

$(2000, 2 M)$

(a) $\sqrt{\frac{m_{1}}{m_{2}}}$

(b) $\sqrt{\frac{m_{2}}{m_{1}}}$

(d) $\frac{m_{2}}{m_{1}}$

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Answer:

Correct Answer: 5. (b)

Solution:

Speed of sound in a gas is given by

$\begin{aligned} v & = \sqrt{\frac{γ R T}{M}}, v \propto \frac{1}{\sqrt{M}} \\ ∴ & \frac{v_{1}}{v_{2}} & = \sqrt{\frac{M_{2}}{M_{1}}} = \sqrt{\frac{m_{2}}{m_{1}}} \end{aligned}$

Here, $γ = \frac{C_{p}}{C_{V}} = \frac{5}{3}$ for both the gases $(γ_{monoatomic} = \frac{5}{3})$

Wave Motion 3 Question 5

5. Two monoatomic ideal gases 1 and 2 of molecular masses $m_{1}$ and $m_{2}$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to the gas 2 is given by

Answer:

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Wave Motion 3 Question 5

5. Two monoatomic ideal gases 1 and 2 of molecular masses m1 and m2 respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to the gas 2 is given by

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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5. Two monoatomic ideal gases 1 and 2 of molecular masses $m_{1}$ and $m_{2}$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to the gas 2 is given by