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The given wave equation is:

\[
y(x, t) = \frac{1}{2} P \sin(4 \pi x - P \pi t + \pi)
\]

where \( P \) is defined as the sum of the third digit and the last digit of a given identifier (NIM), which you specified to be replaced by \( P = 5 \).

This makes the wave equation:

\[
y(x, t) = \frac{1}{2} \cdot 5 \sin(4 \pi x - 5 \pi t + \pi) = \frac{5}{2} \sin(4 \pi x - 5 \pi t + \pi)
\]

Let's address each question:

### (a) Fase Awal Gelombang
The initial phase of the wave is the constant term inside the sine function, which here is \(\pi\). Thus, the initial phase is \(\pi\) radians.

### (b) Fase pada Posisi \( x = 1.5 \, \text{m} \) dan Waktu \( t = 0.25 \, \text{s} \)
To find the phase at \( x = 1.5 \) m and \( t = 0.25 \) s, we substitute these values into the argument of the sine function:
\[
\text{Phase} = 4 \pi (1.5) - 5 \pi (0.25) + \pi
\]
Calculate each term to get the result.

### (c) Kecepatan Perambatan Gelombang
The wave velocity \( v \) for a sinusoidal wave is given by:
\[
v = \frac{\omega}{k}
\]
where \(\omega\) is the angular frequency and \( k \) is the wave number. For the given equation:
- \( k = 4\pi \)
- \(\omega = 5\pi\)

Thus,
\[
v = \frac{5 \pi}{4 \pi} = \frac{5}{4} \, \text{m/s}
\]

### (d) Kecepatan Transversal Maksimum
The maximum transverse velocity \( v_{\text{max}} \) is given by:
\[
v_{\text{max}} = A \omega
\]
where \( A = \frac{5}{2} \) and \( \omega = 5 \pi \). So,
\[
v_{\text{max}} = \frac{5}{2} \cdot 5 \pi = \frac{25 \pi}{2} \, \text{m/s}
\]

### (e) Percepatan Transversal Maksimum
The maximum transverse acceleration \( a_{\text{max}} \) is:
\[
a_{\text{max}} = A \omega^2
\]
Calculating it with \( A = \frac{5}{2} \) and \( \omega = 5 \pi \),
\[
a_{\text{max}} = \frac{5}{2} \cdot (5 \pi)^2 = \frac{5}{2} \cdot 25 \pi^2 = \frac{125 \pi^2}{2} \, \text{m/s}^2
\]

### (f) Kecepatan Transversal di \( x = 2 \, \text{m} \) dan \( t = 1 \, \text{s} \)
To find the transverse velocity, differentiate \( y(x, t) \) with respect to \( t \), then substitute \( x = 2 \) m and \( t = 1 \) s.

### (g) Percepatan Transversal di \( x = 2 \, \text{m} \) dan \( t = 1 \, \text{s} \)
Differentiate the transverse velocity with respect to \( t \) to find the acceleration, then substitute \( x = 2 \) m and \( t = 1 \) s.

### (h) Gambarkan Gelombang
To plot the wave, one would graph \( y(x, t) \) versus \( x \) or \( t \), showing a sinusoidal shape with parameters defined above.

Would you like more detailed calculations or further explanation for any part? 

---

### Related Questions

1. How do you find the wave equation if \( P \) changes?
2. What is the significance of initial phase in wave motion?
3. How does changing \( \omega \) or \( k \) affect wave velocity?
4. What is the difference between phase and phase velocity?
5. How can transverse acceleration be practically observed in a wave?

### Tip
To analyze waves more efficiently, remember that phase velocity \( v \) can be derived from the ratio of angular frequency to wave number.

Calculate various wave properties for the given sinusoidal wave equation with P = 5.

Learn how to calculate wave properties like initial phase, phase at specific points, propagation speed, maximum transverse velocity, and acceleration for a sinusoidal wave equation. Detailed steps provided for understanding wave behavior.

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