A wave is represented by the equation `y=0.5 sin (10 t-x)m`. It is a travelling wave propagating along the + x direction with velocity

Options

A. `10 ms^(-1)`
B. `20 ms^(-1)`
C. `5 ms^(-1)`
D. None of these

Answer

To solve the problem of finding the velocity of the wave represented by the equation \( y = 0.5 \sin(10t - x) \), we can follow these steps:

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

### Step 2: Compare the given equation with the standard form
From the given equation \( y = 0.5 \sin(10t - x) \), we can identify:
- Amplitude \( A = 0.5 \) m,
- Angular frequency \( \omega = 10 \) rad/s,
- The coefficient of \( x \) gives us the wave number \( k = 1 \) rad/m.

### Step 3: Calculate the velocity of the wave
The velocity \( v \) of a traveling wave can be calculated using the formula:
\[ v = \frac{\omega}{k} \]
Substituting the values we identified:
\[ v = \frac{10 \, \text{rad/s}}{1 \, \text{rad/m}} = 10 \, \text{m/s} \]

### Conclusion
The velocity of the wave is \( 10 \, \text{m/s} \).