The equation of a travelling wave is given as `y=5sin10pi(t-Q.01x),` along the x-axis . Here, all quantities are in SI units. The phase difference between the points separated by a distance of 10m alond x-axis is

Options

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

Answer

To find the phase difference between two points separated by a distance of 10 meters 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:
\[ y = 5 \sin(10\pi(t - 0.01x)) \]
This can be rewritten as:
\[ y = 5 \sin(10\pi t - 0.1\pi x) \]

### Step 2: Identify the wave parameters
From the wave equation, we can identify:
- Angular frequency \( \omega = 10\pi \) rad/s
- Wave number \( k = 0.1\pi \) rad/m

### Step 3: Calculate the wavelength
The wave number \( k \) is related to the wavelength \( \lambda \) by the formula:
\[ k = \frac{2\pi}{\lambda} \]
Substituting the value of \( k \):
\[ 0.1\pi = \frac{2\pi}{\lambda} \]
Solving for \( \lambda \):
\[ \lambda = \frac{2\pi}{0.1\pi} = 20 \text{ m} \]

### Step 4: Calculate the phase difference
The phase difference \( \Delta \phi \) between two points separated by a distance \( d \) is given by:
\[ \Delta \phi = k \cdot d \]
Substituting \( k \) and \( d = 10 \text{ m} \):
\[ \Delta \phi = (0.1\pi) \cdot 10 = \pi \]

### Step 5: Conclusion
The phase difference between the two points separated by a distance of 10 meters along the x-axis is:
\[ \Delta \phi = \pi \text{ radians} \]