The velocity of sound in hydrogen at `0^@C` is `1200(m)/(s)`. When some amount of oxygen is mixed with hydrogen, the velocity decreases to `500(m)/(s)`. Determine the ratio of `H_2` to `O_2` by volume in this mixture, given that the density of oxygen in 16 times that of hydrogen.

Explanation

To solve the problem of determining the ratio of hydrogen (H₂) to oxygen (O₂) by volume in a mixture where the velocity of sound changes, we can follow these steps:

### Step 1: Understand the relationship between velocity and density
The velocity of sound (v) in a medium is inversely proportional to the square root of its density (ρ). This can be expressed mathematically as:
\[ v \propto \frac{1}{\sqrt{\rho}} \]
Thus, we can write:
\[ \frac{v_1}{v_2} = \sqrt{\frac{\rho_2}{\rho_1}} \]
where \( v_1 \) is the initial velocity of sound in hydrogen, and \( v_2 \) is the velocity of sound in the mixture.
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