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.