Ratio of amplitude for two wave is 4:15 .Find the ratio of intensity?

Explanation

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

### Step-by-Step Solution:

1. **Identify the Given Data**:
The problem states that the ratio of the amplitudes of two waves is given as:
\[ \frac{A_1}{A_2} = \frac{4}{15} \]

2. **Understand the Relationship Between Intensity and Amplitude**:
The intensity \(I\) of a wave is directly proportional to the square of its amplitude. This can be expressed mathematically as:
\[ I \propto A^2 \]
Therefore, the ratio of intensities can be expressed 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 equation for intensity:
\[ \frac{I_1}{I_2} = \left(\frac{4}{15}\right)^2 \]

4. **Calculate the Square of the Ratio**:
Next, we calculate the square of the ratio:
\[ \frac{I_1}{I_2} = \frac{4^2}{15^2} = \frac{16}{225} \]

5. **State the Final Result**:
Thus, the ratio of the intensities of the two waves is:
\[ \frac{I_1}{I_2} = \frac{16}{225} \]

### Final Answer:
The ratio of intensity \(I_1:I_2\) is \(16:225\).

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