The equuation of a wave is given by
`y=0.5 sin (100 t+25x)`
The ratio of maximum particle velolcity to wave velocity is:

Options

A. 12.5
B. 25
C. 4
D. `1//8`

Explanation

To solve the problem, we need to find the ratio of maximum particle velocity to wave velocity for the wave described by the equation \( y = 0.5 \sin(100t + 25x) \).

### Step-by-Step Solution:

1. **Identify the parameters from the wave equation**:
The wave equation is given in the form \( y = A \sin(\omega t + kx) \).
- Here, \( A = 0.5 \) (amplitude)
- \( \omega = 100 \) (angular frequency)
- \( k = 25 \) (wave number)

2. **Calculate the maximum particle velocity (\( V_{max} \))**:
The maximum particle velocity can be calculated using the formula:
\[ V_{max} = \omega A \]
Substituting the values:
\[ V_{max} = 100 \times 0.5 = 50 \]

3. **Calculate the wave velocity (\( V_{wave} \))**:
The wave velocity can be calculated using the formula:
\[ V_{wave} = \frac{\omega}{k} \]
Substituting the values:
\[ V_{wave} = \frac{100}{25} = 4 \]

4. **Calculate the ratio of maximum particle velocity to wave velocity**:
Now, we find the ratio:
\[ \text{Ratio} = \frac{V_{max}}{V_{wave}} = \frac{50}{4} = 12.5 \]

5. **Final Result**:
The ratio of maximum particle velocity to wave velocity is \( 12.5 \).

### Conclusion:
The correct answer is \( 12.5 \), which corresponds to option 1.