A plane progressive wave is given by `y=3 xx 10^(-7) sin (8500 t-25x)`, where t is in second y is in m. Find the amplitude, and phase difference between two points separated by a distance 0.01m.

Answer

To solve the problem, we need to analyze the given wave equation and extract the required information step by step.

**Step 1: Identify the wave equation**
The wave is given by:
\[ y = 3 \times 10^{-7} \sin(8500 t - 25x) \]

**Step 2: Determine the amplitude**
The general form of a progressive wave is:
\[ y = A \sin(\omega t - kx) \]
where \( A \) is the amplitude, \( \omega \) is the angular frequency, and \( k \) is the wave number.

From the given equation, we can see that:
- The amplitude \( A = 3 \times 10^{-7} \) m.

**Step 3: Find the wave number \( k \)**
From the equation, we can identify:
- \( k = 25 \) (This is the coefficient of \( x \)).

**Step 4: Calculate the phase difference between two points**
The phase difference \( \Delta \phi \) between two points separated by a distance \( \Delta x \) is given by the formula:
\[ \Delta \phi = k \Delta x \]

Given that \( \Delta x = 0.01 \) m, we can substitute the values:
\[ \Delta \phi = 25 \times 0.01 = 0.25 \text{ radians} \]

**Step 5: Convert phase difference to degrees**
To convert radians to degrees, we use the conversion factor:
\[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \]

Thus,
\[ \Delta \phi = 0.25 \times \frac{180}{\pi} \approx 14.32 \text{ degrees} \]

**Final Results:**
- Amplitude \( A = 3 \times 10^{-7} \) m
- Phase difference \( \Delta \phi \approx 0.25 \) radians or \( 14.32 \) degrees

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