This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Here's how to solve the problem: The general equation for a sinusoidal wave traveling in the positive x-direction is given by: y = A ( t - kx) where A is the amplitude, is the angular frequency, and k is the wave number. The given wave equation is: y = 0.002 (300t - 1.5x) Step 1: Compare the given equation with the general wave equation to identify the amplitude, angular frequency, and wave number. From the comparison: A = 0.002 m = 300 rad/s k = 1.5 rad/m a) The amplitude: Step 2: Determine the amplitude (A). The amplitude is directly identified from the equation. A = 0.002 m The amplitude is 0.002 m. b) The frequency: Step 3: Calculate the frequency (f) using the angular frequency . The relationship between angular frequency and frequency is = 2 f. f = ()/(2) Substitute the value of : f = 300 rad/s2 rad f ≈ (300)/(2 × 3.14159) Hz f ≈ 47.746 Hz The frequency is 47.7 Hz. c) The wavelength: Step 4: Calculate the wavelength () using the wave number k. The relationship between wave number and wavelength is k = (2)/(). = (2)/(k) Substitute the value of k: = 2 rad1.5 rad/m ≈ (2 × 3.14159)/(1.5) m ≈ 4.189 m The wavelength is 4.19 m. d) The speed of the wave: Step 5: Calculate the speed of the wave (v). The speed of the wave can be calculated using the formula v = ()/(k). v = 300 rad/s1.5 rad/m v = 200 m/s Alternatively, using v = f: v = (47.746 Hz) × (4.189 m) v ≈ 200 m/s The speed of the wave is 200 m/s. Drop the next question.