The equation of a wave is given by `Y = 5 sin 10pi(t - 0.01x)` along the x-axis. (All the quantities are expressed in SI units). The phase difference between the points separated by a distance of `10 m` along x-axis is

Options

A. `(pi)/(2)`
B. `pi`
C. `2pi`
D. `(pi)/(4)`

Explanation

To find the phase difference between two points separated by a distance of 10 m along the x-axis for the wave described by the equation \( Y = 5 \sin(10\pi(t - 0.01x)) \), we can follow these steps:

### Step 1: Identify the wave equation
The given wave equation is:
\[ Y = 5 \sin(10\pi(t - 0.01x)) \]

### Step 2: Rewrite the wave equation in standard form
The standard form of a wave equation is:
\[ Y = A \sin(\omega t - kx) \]
From the given equation, we can see that:
- \( \omega = 10\pi \)
- \( k = 10\pi \times 0.01 = 0.1\pi \)

### Step 3: Determine the phase difference formula
The phase difference \( \Delta \phi \) between two points separated by a distance \( \Delta x \) is given by:
\[ \Delta \phi = k \Delta x \]

### Step 4: Substitute the values
We know:
- \( k = 0.1\pi \)
- \( \Delta x = 10 \, \text{m} \)

Now, substituting these values into the phase difference formula:
\[ \Delta \phi = (0.1\pi)(10) = 1\pi \]

### Step 5: Final result
Thus, the phase difference between the points separated by a distance of 10 m is:
\[ \Delta \phi = \pi \]

### Conclusion
The correct option is **B: \( \pi \)**.

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