Consider the sound wave travelling in ideal gases of He, and . All the gases have the same ratio , where P is the pressure and is the density. The ratio of the speed of sound through the gases is given by [2025]

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Q.
Consider the sound wave travelling in ideal gases of He, ${CH}_{4}$ and ${CO}_{2}$ . All the gases have the same ratio $\frac{P}{ρ}$ , where P is the pressure and $ρ$ is the density. The ratio of the speed of sound through the gases $V_{He} : V_{{CH}_{4}} : V_{{CO}_{2}}$ is given by [2025]

1 $\sqrt{\frac{7}{5}} : \sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}}$

2 $\sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{7}{5}}$

3 $\sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{4}{3}}$

4 $\sqrt{\frac{4}{3}} : \sqrt{\frac{5}{3}} : \sqrt{\frac{7}{5}}$

Ans.
(3)

$v_{sound} = \sqrt{\frac{γ P}{ρ}}$

$γ = 1 + \frac{2}{f}$

$γ_{He} = 1 + \frac{2}{3} = \frac{5}{3}$

$γ_{{CH}_{4}} = γ_{{CO}_{2}} \approx 1.33 = \frac{4}{3}$

$V_{He} : V_{{CH}_{4}} : V_{{CO}_{2}} = \sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{4}{3}}$

Solution

Q.
Consider the sound wave travelling in ideal gases of He, ${CH}_{4}$ and ${CO}_{2}$ . All the gases have the same ratio $\frac{P}{ρ}$ , where P is the pressure and $ρ$ is the density. The ratio of the speed of sound through the gases $V_{He} : V_{{CH}_{4}} : V_{{CO}_{2}}$ is given by [2025]

1 $\sqrt{\frac{7}{5}} : \sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}}$

2 $\sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{7}{5}}$

3 $\sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{4}{3}}$

4 $\sqrt{\frac{4}{3}} : \sqrt{\frac{5}{3}} : \sqrt{\frac{7}{5}}$

Ans.
(3)

$v_{sound} = \sqrt{\frac{γ P}{ρ}}$

$γ = 1 + \frac{2}{f}$

$γ_{He} = 1 + \frac{2}{3} = \frac{5}{3}$

$γ_{{CH}_{4}} = γ_{{CO}_{2}} \approx 1.33 = \frac{4}{3}$

$V_{He} : V_{{CH}_{4}} : V_{{CO}_{2}} = \sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{4}{3}}$

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Solution

Q. Consider the sound wave travelling in ideal gases of He, CH4 and CO2. All the gases have the same ratio Pρ, where P is the pressure and ρ is the density. The ratio of the speed of sound through the gases VHe : VCH4 : VCO2 is given by [2025]

1 75 : 53 : 43

2 53 : 43 : 75

3 53 : 43 : 43

4 43 : 53 : 75

Ans. (3) vsound=γPρ γ=1+2f γHe=1+23=53 γCH4=γCO2≈1.33=43 VHe : VCH4 : VCO2=53 : 43 : 43

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Q.
Consider the sound wave travelling in ideal gases of He, ${CH}_{4}$ and ${CO}_{2}$ . All the gases have the same ratio $\frac{P}{ρ}$ , where P is the pressure and $ρ$ is the density. The ratio of the speed of sound through the gases $V_{He} : V_{{CH}_{4}} : V_{{CO}_{2}}$ is given by [2025]

1 $\sqrt{\frac{7}{5}} : \sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}}$

2 $\sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{7}{5}}$

3 $\sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{4}{3}}$

4 $\sqrt{\frac{4}{3}} : \sqrt{\frac{5}{3}} : \sqrt{\frac{7}{5}}$

Ans.
(3)

$v_{sound} = \sqrt{\frac{γ P}{ρ}}$

$γ = 1 + \frac{2}{f}$

$γ_{He} = 1 + \frac{2}{3} = \frac{5}{3}$

$γ_{{CH}_{4}} = γ_{{CO}_{2}} \approx 1.33 = \frac{4}{3}$

$V_{He} : V_{{CH}_{4}} : V_{{CO}_{2}} = \sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{4}{3}}$