Pembahasan Soal Gelombang Mekanik | Persamaan Gelombang Berjalan (Fisika Kelas 11) - part 1

Summary

This video tutorial provides an in-depth explanation of mechanical wave equations, focusing on how to analyze and solve problems related to wave propagation. It covers the process of determining various wave properties such as direction of propagation, amplitude, frequency, wavelength, and wave speed. The presenter demonstrates these steps with specific examples, breaking down complex equations and explaining the mathematical relationships involved. Additionally, the video explains the use of graphical representations to derive wave equations and emphasizes the application of key formulas for understanding wave mechanics.

Takeaways

• 😀 The direction of wave propagation is determined by the sign of the wave's equation. A negative sign indicates the wave moves to the right.
• 😀 The amplitude of the wave is 0.2 cm, as indicated by the coefficient of the sine function in the equation.
• 😀 To find the frequency of the wave, use the formula Omega = 2πf, where Omega is the angular frequency, which in this case is 24π. This results in a frequency of 12 Hz.
• 😀 The wavelength of the wave can be calculated using the value of the wave number (k), which is 0.4π in this case. The wavelength comes out to be 5 cm.
• 😀 The wave speed (v) is found by multiplying the frequency and wavelength, giving a result of 60 cm/s.
• 😀 The equation for a traveling wave can be derived from its general form, y = A sin(ωt - kx), where A is the amplitude, ω is angular frequency, and k is the wave number.
• 😀 In another example, the number of complete wave cycles within a given time interval is used to find the frequency. For 2 complete waves over 5 seconds, the frequency is calculated as 0.4 Hz.
• 😀 The phase constant (k) is found by using the relationship k = 2π/λ, where λ is the wavelength, which is determined to be 2 meters in this example.
• 😀 The angular frequency Omega is calculated as 0.8π radians per second using the formula 2π times the frequency.
• 😀 For waves moving to the left, the wave equation includes a positive sign in front of the x-term (ωt + kx), indicating the direction of propagation.
• 😀 The wave equation for the second example is y = -6 sin(0.8πt + 0.01x), where the negative sign indicates that the wave is traveling to the left, and the amplitude is 6 cm.

Q & A

What is the general form of the wave equation presented in the script?

The general form of the wave equation presented is y = 0.20 sin(0.40t - x), where x and y are in centimeters, and t is in seconds.

How do you determine the direction of wave propagation from the equation?

The direction of propagation is determined by the sign in front of the x term in the wave equation. If the sign is negative, the wave propagates to the right, and if the sign is positive, the wave propagates to the left.

What is the amplitude of the wave in the first problem?

The amplitude of the wave is 0.2 cm, which is the coefficient of the sine function in the equation.

How is the frequency of the wave calculated from the angular frequency?

The frequency (f) is calculated using the formula f = ω / 2π, where ω is the angular frequency. In the script, ω is given as 24π, so f = 24π / 2π = 12 Hz.

What formula is used to find the wavelength from the wave number (k)?

The wavelength (λ) is found using the formula λ = 2π / k, where k is the wave number. In the script, k = 0.4π, so λ = 2π / 0.4π = 5 cm.

How do you calculate the wave speed from the frequency and wavelength?

The wave speed (v) is calculated using the formula v = f * λ, where f is the frequency and λ is the wavelength. In the script, v = 12 Hz * 5 cm = 60 cm/s.

What does the negative sign in the amplitude of the second wave equation indicate?

The negative sign in the amplitude indicates that the wave starts at its lowest point, meaning the amplitude is directed downward initially.

How is the frequency of the wave determined from the number of complete waves and the time interval?

The frequency is determined by dividing the number of complete waves by the total time interval. In the second problem, 2 complete waves occur in 5 seconds, so the frequency is 2 / 5 = 0.4 Hz.

What is the value of the angular frequency (ω) for the second wave equation?

The angular frequency (ω) is calculated using the formula ω = 2π * f. With a frequency of 0.4 Hz, ω = 2π * 0.4 = 0.8π radians per second.

What is the wavelength of the second wave, and how is it calculated?

The wavelength (λ) is 2 meters, which is calculated by dividing the total distance (4 meters for two complete waves) by 2. Thus, λ = 4 m / 2 = 2 m, or 200 cm.