A travelling wave of amplitude `5 A` is partically reflected from a bounday with the amplitude `3A`. Due to superposition of two waves with different amplitude in opposite direction a standing wave pattern is formed. Datermine the ratio of amplitude at antinode to node.

Explanation

To solve the problem of determining the ratio of amplitude at the antinode to that at the node for the given traveling wave scenario, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amplitudes**:
- The amplitude of the incident wave (\(A_i\)) is given as \(5A\).
- The amplitude of the reflected wave (\(A_r\)) is given as \(3A\).

2. **Calculate the Amplitude at the Node**:
- The amplitude at the node (\(A_n\)) is calculated using the formula:
\[ A_n = A_i - A_r \]
- Substituting the given values:
\[ A_n = 5A - 3A = 2A \]

3. **Calculate the Amplitude at the Antinode**:
- The amplitude at the antinode (\(A_{an}\)) is calculated using the formula:
\[ A_{an} = A_i + A_r \]
- Substituting the given values:
\[ A_{an} = 5A + 3A = 8A \]

4. **Determine the Ratio of Amplitude at Antinode to Node**:
- The ratio (\(R\)) of the amplitude at the antinode to that at the node is given by:
\[ R = \frac{A_{an}}{A_n} \]
- Substituting the calculated amplitudes:
\[ R = \frac{8A}{2A} = 4 \]

5. **Final Result**:
- Therefore, the ratio of the amplitude at the antinode to the amplitude at the node is \(4\).

### Summary:
The ratio of amplitude at antinode to node is \(4\).