A standing wave is represented by, `y-Asin(100t)cos(0.01x)`, where x,y and A are in millimeter and t in second. The velocity of the wave is

Options

A. `10^(4)` m/s
B. Not derivable
C. 1 m/s
D. `10^(2)` m/s

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 and Wave Number
The general form of a standing wave can be expressed as:
\[ y = A \sin(\omega t) \cos(kx) \]
where:
- \( \omega \) is the angular frequency,
- \( k \) is the wave number.

From the given equation \( y = A \sin(100t) \cos(0.01x) \), we can identify:
- \( \omega = 100 \) (the coefficient of \( t \)),
- \( k = 0.01 \) (the coefficient of \( x \)).

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

Substituting the values we found:
\[ v = \frac{100}{0.01} \]

### Step 3: Perform the Calculation
Calculating the above expression:
\[ v = 100 \div 0.01 = 10000 \, \text{mm/s} \]

### Step 4: Convert to Standard Units
Since the question specifies that \( x \) and \( y \) are in millimeters, we can convert the velocity to meters per second:
\[ v = 10000 \, \text{mm/s} = 10 \, \text{m/s} \]

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

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