Ratio of amplitude for two wave is 11:4.Find the ratio of intensity?

Explanation

To solve the problem, we need to find the ratio of intensity based on the given ratio of amplitudes for two waves. Here’s a step-by-step solution:

### Step 1: Write down the given data
We are given the ratio of amplitudes of two waves:
\[ \frac{A_1}{A_2} = \frac{11}{4} \]

### Step 2: Understand the relationship between intensity and amplitude
We know that the intensity \( I \) of a wave is directly proportional to the square of its amplitude. This can be expressed mathematically as:
\[ I \propto A^2 \]
Thus, the ratio of intensities \( \frac{I_1}{I_2} \) can be expressed in terms of the ratio of amplitudes:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

### Step 3: Substitute the ratio of amplitudes into the intensity ratio formula
Now we substitute the given ratio of amplitudes into the intensity ratio formula:
\[ \frac{I_1}{I_2} = \left(\frac{11}{4}\right)^2 \]

### Step 4: Calculate the square of the ratio
Now we calculate the square:
\[ \frac{I_1}{I_2} = \frac{11^2}{4^2} = \frac{121}{16} \]

### Step 5: State the final answer
Thus, the ratio of intensities \( I_1 : I_2 \) is:
\[ \frac{I_1}{I_2} = \frac{121}{16} \]

### Conclusion
The final answer is:
\[ I_1 : I_2 = 121 : 16 \]

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