Math Problem Statement
P diganti dengan 5
Solution
The given wave equation is:
where 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 .
This makes the wave equation:
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 . Thus, the initial phase is radians.
(b) Fase pada Posisi dan Waktu
To find the phase at m and s, we substitute these values into the argument of the sine function: Calculate each term to get the result.
(c) Kecepatan Perambatan Gelombang
The wave velocity for a sinusoidal wave is given by: where is the angular frequency and is the wave number. For the given equation:
Thus,
(d) Kecepatan Transversal Maksimum
The maximum transverse velocity is given by: where and . So,
(e) Percepatan Transversal Maksimum
The maximum transverse acceleration is: Calculating it with and ,
(f) Kecepatan Transversal di dan
To find the transverse velocity, differentiate with respect to , then substitute m and s.
(g) Percepatan Transversal di dan
Differentiate the transverse velocity with respect to to find the acceleration, then substitute m and s.
(h) Gambarkan Gelombang
To plot the wave, one would graph versus or , showing a sinusoidal shape with parameters defined above.
Would you like more detailed calculations or further explanation for any part?
Related Questions
- How do you find the wave equation if changes?
- What is the significance of initial phase in wave motion?
- How does changing or affect wave velocity?
- What is the difference between phase and phase velocity?
- How can transverse acceleration be practically observed in a wave?
Tip
To analyze waves more efficiently, remember that phase velocity can be derived from the ratio of angular frequency to wave number.
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Math Problem Analysis
Mathematical Concepts
Wave Motion
Trigonometry
Calculus
Sinusoidal Waves
Formulas
Wave Equation: y(x, t) = A sin(kx - ωt + φ)
Wave Velocity: v = ω / k
Maximum Transverse Velocity: v_max = Aω
Maximum Transverse Acceleration: a_max = Aω^2
Phase Calculation: ϕ = kx - ωt + φ
Theorems
-
Suitable Grade Level
Undergraduate Physics
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