The speed of sound is `330 ms^(-1)` and that of light is `3 xx 10^(8) ms^(-1)`. The ratio of speed of sound to that of light is `11 : 10^x`. Find the value of x.

Explanation

To find the value of \( x \) in the ratio of the speed of sound to the speed of light, we can follow these steps:

### Step 1: Write down the given values
The speed of sound is given as:
\[ v_{sound} = 330 \, \text{m/s} \]
The speed of light is given as:
\[ v_{light} = 3 \times 10^8 \, \text{m/s} \]

### Step 2: Set up the ratio
We need to find the ratio of the speed of sound to the speed of light:
\[ \text{Ratio} = \frac{v_{sound}}{v_{light}} = \frac{330}{3 \times 10^8} \]

### Step 3: Simplify the ratio
To simplify the ratio, we can divide both the numerator and the denominator:
\[ \frac{330}{3 \times 10^8} = \frac{330 \div 3}{10^8} = \frac{110}{10^8} \]

### Step 4: Express the ratio in terms of powers of 10
Now, we can express \( 110 \) in terms of powers of ten:
\[ \frac{110}{10^8} = \frac{11 \times 10^1}{10^8} = \frac{11}{10^7} \]

### Step 5: Set the ratio equal to the given ratio
According to the problem, this ratio can be expressed as:
\[ \frac{11}{10^x} \]
So we have:
\[ \frac{11}{10^7} = \frac{11}{10^x} \]

### Step 6: Equate the exponents
Since the numerators are equal, we can equate the denominators:
\[ 10^7 = 10^x \]
This implies that:
\[ x = 7 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{7} \]

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