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

Options

A. `100m//s`
B. `250m//s`
C. `750m//s`
D. `1000 m//s`

Explanation

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

### Step 1: Identify the parameters from the wave equation
The given wave equation can be compared with the standard form of a wave equation:
\[ y = A \sin(\omega t - kx) \]
From the given equation \( y = 10^{-4} \sin \left( 100t - \frac{x}{10} \right) \), we can identify:
- \( \omega = 100 \) (angular frequency)
- \( k = \frac{1}{10} \) (wave number)

### Step 2: Calculate the frequency \( f \)
The frequency \( f \) can be calculated from the angular frequency \( \omega \) using the formula:
\[ f = \frac{\omega}{2\pi} \]
Substituting the value of \( \omega \):
\[ f = \frac{100}{2\pi} \]

### Step 3: Calculate the wavelength \( \lambda \)
The wavelength \( \lambda \) can be calculated from the wave number \( k \) using the formula:
\[ \lambda = \frac{2\pi}{k} \]
Substituting the value of \( k \):
\[ \lambda = \frac{2\pi}{\frac{1}{10}} = 20\pi \]

### Step 4: Calculate the wave velocity \( v \)
The wave velocity \( v \) can be calculated using the formula:
\[ v = f \cdot \lambda \]
Substituting the values of \( f \) and \( \lambda \):
\[ v = \left( \frac{100}{2\pi} \right) \cdot (20\pi) \]
Simplifying:
\[ v = \frac{100 \cdot 20\pi}{2\pi} = \frac{2000\pi}{2\pi} = 1000 \, \text{m/s} \]

### Final Answer
The velocity of the wave is \( v = 1000 \, \text{m/s} \).

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