Ratio of amplitude for two wave is 15:9.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 1: Understand the relationship between amplitude and intensity
We know that the intensity (I) of a wave is proportional to the square of its amplitude (A). This can be expressed mathematically as:
\[ I \propto A^2 \]

### Step 2: Write the given data
From the problem, we are given the ratio of amplitudes of two waves:
\[ \frac{A_1}{A_2} = \frac{15}{9} \]

### Step 3: Write the formula for the ratio of intensities
Using the relationship between intensity and amplitude, we can express the ratio of intensities as:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

### Step 4: Substitute the values into the formula
Now we can substitute the given ratio of amplitudes into the formula:
\[ \frac{I_1}{I_2} = \left(\frac{15}{9}\right)^2 \]

### Step 5: Calculate the square of the ratio
Calculating the square of the ratio:
\[ \frac{I_1}{I_2} = \frac{15^2}{9^2} = \frac{225}{81} \]

### Step 6: Final result
Thus, the ratio of intensities is:
\[ \frac{I_1}{I_2} = \frac{225}{81} \]