ExamBro
ExamBro
MHT CET · Physics · Waves and Sound

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

  1. A \(1: 1\)
  2. B \(7 ; 3\)
  3. C \(21: 25\)
  4. D \(\sqrt{42}: 5\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\sqrt{42}: 5\)

Step-by-step Solution

Detailed explanation

Formula:
\(\frac{v_H}{v_{H e}}=\sqrt{\frac{\gamma_H M_{H e}}{\gamma_{H e} M_H}} .\)
Given:
- \(\gamma_H=\frac{7}{5}, \gamma_{H e}=\frac{5}{3}\),
- \(M_H=2, M_{H e}=4\).
Step 1: Substitute values:
\(\frac{v_H}{v_{H e}}=\sqrt{\frac{\frac{7}{5} \cdot 4}{\frac{5}{3} \cdot 2}}=\sqrt{\frac{28}{10} \cdot \frac{3}{5}}=\sqrt{\frac{84}{50}}=\frac{\sqrt{42}}{5} .\)
Answer: \(\frac{\sqrt{42}}{5}\), Option 4.