The equation of a wave is `y=5sin((t)/(0.04)-(x)/(4))` where `x` is in cm and t is in seccond. The velocity of the wave will be

Options

A. `1ms^(-1)`
B. `2ms^(-1)`
C. `1.5ms^(-1)`
D. `1.25ms^(-1)`

Explanation

To find the velocity of the wave given by the equation \( y = 5 \sin\left(\frac{t}{0.04} - \frac{x}{4}\right) \), we will 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:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number.

### Step 2: Compare the given equation with the general form
From the given equation:
\[ y = 5 \sin\left(\frac{t}{0.04} - \frac{x}{4}\right) \]
we can identify:
- \( \omega = \frac{1}{0.04} \)
- \( k = \frac{1}{4} \)

### Step 3: Calculate the values of \( \omega \) and \( k \)
Calculating \( \omega \):
\[ \omega = \frac{1}{0.04} = 25 \, \text{rad/s} \]

Calculating \( k \):
\[ k = \frac{1}{4} \, \text{rad/cm} \]

### Step 4: Use the relationship between \( \omega \), \( k \), and wave velocity \( v \)
The relationship is given by:
\[ v = \frac{\omega}{k} \]

### Step 5: Substitute the values of \( \omega \) and \( k \)
Substituting the values:
\[ v = \frac{25}{\frac{1}{4}} = 25 \times 4 = 100 \, \text{cm/s} \]

### Step 6: Convert the velocity to meters per second
Since the question asks for the velocity in meters per second, we convert:
\[ 100 \, \text{cm/s} = 1 \, \text{m/s} \]

### Final Answer
The velocity of the wave is:
\[ \boxed{1 \, \text{m/s}} \]

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