The equation of a wave is given by
`y=a sin (100t-x/10)` where x and y are in metre an t in second, the velocity of wave is

Options

A. 0.1m/s
B. 10 m/s
C. 100m/s
D. 1000 m/s

Answer

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

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

### Step 2: Compare with the given equation
From the given equation \( y = a \sin(100t - \frac{x}{10}) \), we can identify:
- \( \omega = 100 \) (coefficient of \( t \))
- \( k = \frac{1}{10} \) (coefficient of \( x \))

### Step 3: Use the relationship between velocity, angular frequency, and wave number
The velocity \( v \) of the wave can be calculated using the formula:
\[ v = \frac{\omega}{k} \]

### Step 4: Substitute the values of \( \omega \) and \( k \)
Substituting the values we found:
\[ v = \frac{100}{\frac{1}{10}} \]

### Step 5: Simplify the expression
Calculating the above expression:
\[ v = 100 \times 10 = 1000 \, \text{m/s} \]

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

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