Ratio of amplitude for two wave is 7:11 .Find the ratio of intensity?

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Write down the given data
We are given the ratio of amplitudes of two waves, which is:
\[ \frac{A_1}{A_2} = \frac{7}{11} \]

### 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 formula:
\[ \frac{I_1}{I_2} = \left(\frac{7}{11}\right)^2 \]

### Step 4: Calculate the square of the ratio
Now we calculate the square of \( \frac{7}{11} \):
\[ \frac{I_1}{I_2} = \frac{7^2}{11^2} = \frac{49}{121} \]

### Step 5: State the final answer
Thus, the ratio of intensities \( I_1 : I_2 \) is:
\[ \frac{I_1}{I_2} = \frac{49}{121} \]