Step 2: Recognize that the general form of a wave equation is y(x, t) = A sin(kx - ωt), where A is amplitude, k is the wave number, and ω is the angular frequency.
Step 3: From the equation, identify k and ω. Here, k = 2π * 0.5 and ω = 2π * 10.
Step 4: Calculate the wave number k: k = 2π * 0.5 = π.
Step 5: Calculate the angular frequency ω: ω = 2π * 10 = 20π.
Step 6: Find the frequency f using the formula f = ω / (2π): f = (20π) / (2π) = 10 Hz.
Step 7: Calculate the wavelength λ using the formula k = 2π / λ: λ = 2π / k = 2π / π = 2 m.
Step 8: Use the wave speed formula v = f * λ: v = 10 Hz * 2 m = 20 m/s.
Wave Equation Analysis – Understanding the wave equation and identifying parameters such as frequency and wavelength.
Wave Speed Calculation – Using the relationship between wave speed, frequency, and wavelength to calculate the speed of the wave.
