A standing wave is represeneted by `y=asin (100t)cos (0.01)x` in second and x is in ,metre. Velocity of wave is

Options

A. `10 ^(4)` m/s
B. `1` m/s
C. `10` m/s
D. none of these

Answer

To find the velocity of the standing wave represented by the equation \( y = a \sin(100t) \cos(0.01x) \), we can follow these steps:

### Step 1: Identify the angular frequency (\( \omega \)) and the wave number (\( k \))
From the given equation, we can identify:
- The angular frequency \( \omega = 100 \) (from the term \( \sin(100t) \))
- The wave number \( k = 0.01 \) (from the term \( \cos(0.01x) \))

### Step 2: Use the formula for wave velocity
The velocity \( v \) of a wave can be calculated using the formula:
\[ v = \frac{\omega}{k} \]

### Step 3: Substitute the values of \( \omega \) and \( k \)
Now, substituting the values we identified:
\[ v = \frac{100}{0.01} \]

### Step 4: Calculate the velocity
Calculating the above expression:
\[ v = 100 \div 0.01 = 10000 \text{ m/s} \]

### Conclusion
Thus, the velocity of the wave is \( 10000 \text{ m/s} \).

---