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 wave number (\( k \))
The given wave equation is in the form:
\[ y = a \sin(\omega t) \cos(kx) \]
From the equation \( y = a \sin(100t) \cos(0.01x) \), we can identify:
- \( \omega = 100 \) (angular frequency in radians per second)
- \( k = 0.01 \) (wave number in radians per meter)

### 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: Perform the calculation
Calculating the above expression:
\[ v = \frac{100}{0.01} = 10000 \, \text{m/s} \]

### Final Answer
The velocity of the wave is:
\[ v = 10^4 \, \text{m/s} \]

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