If the ratio of amplitude of two waves is `4:3`, then the ratio of maximum and minimum intensity is

Answer

To solve the problem of finding the ratio of maximum and minimum intensity given the ratio of amplitudes of two waves as \(4:3\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The relationship between maximum intensity (\(I_{max}\)) and minimum intensity (\(I_{min}\)) in terms of the amplitudes of two waves (\(A_1\) and \(A_2\)) is given by the formula:
\[ \frac{I_{max}}{I_{min}} = \left( \frac{A_1 + A_2}{A_1 - A_2} \right)^2 \]

2. **Assign Amplitudes**: From the problem, we know the ratio of the amplitudes is \(4:3\). We can assign:
\[ A_1 = 4 \quad \text{and} \quad A_2 = 3 \]

3. **Substitute into the Formula**: Plugging the values of \(A_1\) and \(A_2\) into the formula:
\[ \frac{I_{max}}{I_{min}} = \left( \frac{4 + 3}{4 - 3} \right)^2 \]

4. **Calculate the Numerator and Denominator**:
- The numerator \(4 + 3 = 7\)
- The denominator \(4 - 3 = 1\)

5. **Simplify the Expression**: Now substitute these values back into the equation:
\[ \frac{I_{max}}{I_{min}} = \left( \frac{7}{1} \right)^2 = 7^2 = 49 \]

6. **Write the Final Ratio**: Therefore, the ratio of maximum intensity to minimum intensity is:
\[ I_{max} : I_{min} = 49 : 1 \]

### Final Answer:
The ratio of maximum and minimum intensity is \(49:1\).