Circle the correct answer for each question Which of the following displacement

Question

Circle the correct answer for each 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 = 0.0035 kg/m, M - 6.00 kg and L = 3.50 m. Find the speed of a transverse wave in the string. 15 m/s, 130 m/s, 121 m/s, 112 m/s For the string in problem 2, what is the frequency of the third harmonic? 84 Hz, 90 Hz, 56 Hz. 121 Hz For the string in problem 2, what will be the distance from the wall to the left-most node in string when it vibrates at the frequency of the third harmonic? 1.167m, 0.500m, 0.667m 0.833 m For the string in problem 2, what is the wavelength of the eighth 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 = 0.0025 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

1) correct option is (b)

2) u = 0.0035 kg/m , M = 6 kg, L = 3.5 m

v = (T/u)^0.5

v = (6*9.8/0.0035)^0.5 =130 m/s

correct option is (b)

3) f = nv/2L

f = 3*130/(2*3.5 ) = 56 Hz

4) lamda = 2L/3

distance between two nodes is lamda/2

x = L/3 = 3.5/3 = 1.167 m

correct option is (a)

5) lamda = 2L/8 = 2*3.5/8 = 0.875 m

correct otpion is (a)

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