In interference, two individual amplitudes are 5 units and 3 units. Find
(a)`A_(max)/A_(min)` (b) ` I_(max)/I_(min)` .

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given amplitudes
Let the amplitudes of the two waves be:
- \( A_1 = 5 \) units (Amplitude of wave 1)
- \( A_2 = 3 \) units (Amplitude of wave 2)

### Step 2: Calculate the maximum and minimum amplitudes
The maximum amplitude \( A_{max} \) and minimum amplitude \( A_{min} \) in interference can be calculated using the formulas:
- \( A_{max} = A_1 + A_2 \)
- \( A_{min} = |A_1 - A_2| \)

Substituting the values:
- \( A_{max} = 5 + 3 = 8 \)
- \( A_{min} = |5 - 3| = 2 \)

### Step 3: Calculate the ratio \( \frac{A_{max}}{A_{min}} \)
Now, we can find the ratio of maximum amplitude to minimum amplitude:
\[ \frac{A_{max}}{A_{min}} = \frac{8}{2} = 4 \]

### Step 4: Calculate the maximum and minimum intensities
The intensity of a wave is proportional to the square of its amplitude. Therefore, the maximum intensity \( I_{max} \) and minimum intensity \( I_{min} \) can be calculated as:
- \( I_{max} \propto A_{max}^2 \)
- \( I_{min} \propto A_{min}^2 \)

Calculating the squares:
- \( I_{max} \propto 8^2 = 64 \)
- \( I_{min} \propto 2^2 = 4 \)

### Step 5: Calculate the ratio \( \frac{I_{max}}{I_{min}} \)
Now, we can find the ratio of maximum intensity to minimum intensity:
\[ \frac{I_{max}}{I_{min}} = \frac{64}{4} = 16 \]

### Final Answers
(a) \( \frac{A_{max}}{A_{min}} = 4 \)
(b) \( \frac{I_{max}}{I_{min}} = 16 \)

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