Ratio of amplitude for two wave is 2:15 .Find the ratio of intensity?

Explanation

To solve the problem of finding the ratio of intensity given the ratio of amplitudes of two waves, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
The ratio of amplitudes for the two waves is given as:
\[ \frac{A_1}{A_2} = \frac{2}{15} \]

2. **Understand the Relationship Between Intensity and Amplitude:**
We know that intensity (I) is directly proportional to the square of the amplitude (A). This can be expressed mathematically as:
\[ I \propto A^2 \]
Therefore, the ratio of intensities can be written as:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

3. **Substitute the Given Ratio of Amplitudes:**
Now, we substitute the given ratio of amplitudes into the intensity ratio equation:
\[ \frac{I_1}{I_2} = \left(\frac{2}{15}\right)^2 \]

4. **Calculate the Square of the Ratio:**
Now we calculate the square of the fraction:
\[ \left(\frac{2}{15}\right)^2 = \frac{2^2}{15^2} = \frac{4}{225} \]

5. **State the Final Result:**
Therefore, the ratio of the intensities \( I_1 \) to \( I_2 \) is:
\[ \frac{I_1}{I_2} = \frac{4}{225} \]

### Final Answer:
The ratio of intensity \( I_1 : I_2 \) is \( 4 : 225 \).

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