Final answer:
The speed of a point on a string at half the maximum displacement of a sinusoidal wave is approximately 0.866 times the maximum speed of the string (v = 0.866 * V_{s}).
Step-by-step explanation:
The question is asking about the speed of a point on a string carrying a sinusoidal wave when the displacement is at half of its maximum value. The phenomenon can be explained through the principles of simple harmonic motion (SHM), which states that the speed of an oscillator is dependent on the displacement from its equilibrium position. When the displacement is at half the maximum amplitude (y = A/2), we can use the SHM relationship v = ±√(V_{s}^{2} - (2πf)^{2}y^{2}) where V_{s} is the maximum speed, f is the frequency, and y is the displacement. The equation simplifies, considering the displacement is half the maximum amplitude, thus the speed of the point is v = 0.866 * V_{s}.