The equation of a wave is represented by `y=10^-4sin[100t-(x)/(10)]`. The velocity of the wave will be

Options

A. 100 m/s
B. 4 m/s
C. 1000 m/s
D. 0.00 m/s

Answer

To find the velocity of the wave represented by the equation \( y = 10^{-4} \sin(100t - \frac{x}{10}) \), we can follow these steps:

### Step 1: Identify the parameters from the wave equation
The general form of a progressive wave is given by:
\[ y = A \sin(\omega t - kx) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number.

From the given equation, we can identify:
- \( \omega = 100 \) (coefficient of \( t \))
- \( k = \frac{1}{10} \) (coefficient of \( x \))

### Step 2: Calculate the wave number \( k \)
The wave number \( k \) is related to the wavelength \( \lambda \) by the formula:
\[ k = \frac{2\pi}{\lambda} \]
From our identification, we have:
\[ k = \frac{1}{10} \]
Setting these equal gives:
\[ \frac{1}{10} = \frac{2\pi}{\lambda} \]
Rearranging for \( \lambda \):
\[ \lambda = 2\pi \times 10 = 20\pi \]

### Step 3: Calculate the angular frequency \( \omega \)
The angular frequency \( \omega \) is related to the frequency \( f \) by:
\[ \omega = 2\pi f \]
From our identification, we have:
\[ \omega = 100 \]
Setting these equal gives:
\[ 100 = 2\pi f \]
Rearranging for \( f \):
\[ f = \frac{100}{2\pi} = \frac{50}{\pi} \]

### Step 4: Calculate the velocity \( v \)
The velocity \( v \) of the wave can be calculated using the formula:
\[ v = f \lambda \]
Substituting the values we found:
\[ v = \left(\frac{50}{\pi}\right) \times (20\pi) = 50 \times 20 = 1000 \, \text{m/s} \]

### Final Answer
Thus, the velocity of the wave is:
\[ \boxed{1000 \, \text{m/s}} \]