Ratio of amplitude for two wave is 8:7 .Find the ratio of intensity?

Explanation

To find the ratio of intensity given the ratio of amplitudes, we can follow these steps:

### Step 1: Understand the relationship between amplitude and intensity
Intensity (I) of a wave is directly proportional to the square of its amplitude (A). Mathematically, this can be expressed as:
\[ I \propto A^2 \]

### Step 2: Write down the given data
From the problem, we know the ratio of the amplitudes of two waves:
\[ \frac{A_1}{A_2} = \frac{8}{7} \]

### Step 3: Express 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 given ratio of amplitudes
Now, substituting the given ratio of amplitudes into the equation:
\[ \frac{I_1}{I_2} = \left( \frac{8}{7} \right)^2 \]

### Step 5: Calculate the square of the ratio
Calculating the square of the ratio:
\[ \frac{I_1}{I_2} = \frac{8^2}{7^2} = \frac{64}{49} \]

### Step 6: State the final answer
Thus, the ratio of intensities \( I_1 : I_2 \) is:
\[ \frac{I_1}{I_2} = \frac{64}{49} \]