Which of the following displacement functions for a string is not a solution to

Question

Which of the following displacement functions for a string is not a solution to the wave equation? y(x, t) = A sin (K (x + ct)), y(x, t) = A sin(kx) sin(kct), y(x, t) = A (sin(kx) + sin(kct)), y(x, t) = A(sin(kx - kct) + sin(kx + kct)). A string of mass/length mu is connected to a hanging mass M. The left end is connected to a wall and the right end passes over a frictionless pulley, as shown in the diagram. The length of the horizontal segment is L. Let mu = 0.0025 kg/m, M = 3.20 kg and L = 2.00 m. Find the speed of a transverse wave in the string 150 m/s, 130 m/s, 121 m/s, 112 m/s For the string in problem 2, what is the frequency the third harmonic? 84 Hz. 90 Hz, 56 Hz, 121 Hz For the string in problem 2, what will be distance from the wall to the left-most node in the string when it vibrates at the frequency of the third harmonic? 1.167 m, 0.500 m, 0.667 m, 0.833 m. For the string in problem 2, what is the wavelength of the sixth harmonic? 0.875 0.600 m, 0.667 m, 0.714 m For the string in problem 2, how much energy is stored in the fundamental mode if the amplitude of the transverse displacement is y_m 0.0035 m? 4.74 times 10^-4 J, 3.48 times 10^-4 J, 2.59 times 10^-4 J, 7.74 times 10^-4 J

Explanation / Answer

Mass = m = 3.2 kg

Mass/length = u = 0.0025 kg/m

Speed = v = sqrt(mg/u) = sqrt(3.2*9.8/0.0025) = 112 m/s (Option d)

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