Question

The speed of sound in hydrogen is 1270 m/s. The speed of sound in the mixture of oxygen and hydrogen in which they are mixed in 1:4 ratio is

Options

• 600 m/s

• 635 m/s

• 640 m/s

• 660 m/s

Answer 1

635 m/s

Explanation:

Let V₁ and V₂ represent the volume of oxygen and hydrogen, respectively.

Let p₁, m₁ represent the mass and density of oxygen in the mixture, and p₂, m₂ represent the mass and density of hydrogen.

∴ p = `"Total mass"/"Total volume" = (V_1p_1 + V_2P_2)/(V_1 + V_2)`

p = `(V_2p_2 ((V_1p_1)/(V_2p_2) + 1))/(V_2(V_1/V_2 + 1))`

= `(p_2(V_1/V_2 * p_1/p_2 + 1))/((V_1/V_2 + 1))`

p = `(p_2(1/4 xx 16 + 1))/((1/4 + 1))`  .....`[because  V_1/V_2 = 1/4 "and" p_1/p_2 = 32/2 = 16]`

= 4 p₂ 

⇒ `p/p_2` = 4

Let v₁ and v₂ represent the sound speed for hydrogen and the mixture, respectively.

v₁ = `sqrt((ϒP)/p` and v₂ = `sqrt((ϒP)/(p_2)`

∴ `v_1/v_2 = sqrt(p_2/p)`

v₁ = `(sqrt(1/4))` v₂ = `v_2/2 = 1270/2` = 635 m/sec