Here are the essential concepts you must grasp in order to answer the question correctly.
Wave Equation
The wave equation describes the behavior of waves, including their amplitude, wavelength, and frequency. In the given equation D(x,t) = (2.00 cm) × sin[(12.57 rad/m)x - (638 rad/s)t], the amplitude is 2.00 cm, the wave number is 12.57 rad/m, and the angular frequency is 638 rad/s. Understanding these parameters is essential for analyzing wave properties and their effects on the medium.
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Maximum Speed of a Point on the String
The maximum speed of a point on the string can be determined from the wave's properties. It is given by the formula v_max = Aω, where A is the amplitude and ω is the angular frequency. In this case, the amplitude is 2.00 cm (0.02 m) and the angular frequency is 638 rad/s, allowing us to calculate the maximum speed of the oscillating points on the string.
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Linear Density
Linear density is defined as the mass per unit length of a string, which affects how waves propagate through it. In this problem, the linear density is given as 5.00 g/m (or 0.005 kg/m). This property is crucial for understanding wave speed and tension in the string, as it influences the wave's behavior and the energy transmission along the medium.
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