A standing wave is set up on a string of length L, fixed at both ends. If 6 nodes and 5 antinodes are observed when the wavelength is A = 1.8 m, then the length of the string is: O L= 2.35 m O L= 5.40 m L= 6.48 m L = 3.75 m O L=4.50 m
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A: Here, we apply superposition and analyse the resultant wave.
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- Two harmonic waves, y1 = A sin(kx − ωt) and y2 = A sin(kx + ωt + φ), travel in the same string creating a standing wave pattern. If φ = 2.60 rad and λ = 3.36 m, find the position of the first node for which the position x > 0.The wave function of a sinusoidal wave generated in a string is given by: y(x,t) = 0.2 sin (2èx + 4rt + p). At t = 0, an element of the string at x = 0 has a vertical displacement of 0.2 m. The phase constant is: O p = π/2 4 = -π/4 4 = -π/2 φ = π 4=0A standing wave has the following wave-function: y(x,t) = 0.2 sin(πx) cos(12πt), where x and y are in meters, and t is in seconds. If the length of the string is L = 2 m and it is fixed at both ends, then the harmonic, n, in which the string is vibrating is: n = 4 n = 2 n = 3 n = 6 n = 5
- A transverse wave on a string is described by y(x, t) = (0.480 mm) sin {(2.747 rad/m)[x − (68.1 m/s)t]}. In what direction does the wave travel?A transverse wave on a string is described by y(x, t) = (0.480 mm) sin {(2.747 rad/m)[x − (68.1 m/s)t]}. What is the maximum transverse speed of a point on the string?Two waves are traveling in opposite directions on the same string. The displacements caused by the individiual waves are given by y1=(21.0 mm)sin(6.70πt - 1.16πx) and y2=(39.0 mm)sin(3.70πt + 0.211πx). Note that the phase angles (6.70πt - 1.16πx) and (3.70πt + 0.211πx) are in radians, t is in seconds, and x is in meters. At t = 2.10 s, what is the net displacement (in mm) of the string at (a) x = 2.25 m and (b) x = 2.54 m? Be sure to include the algebraic sign (+ or -) with your answers.
- A wave with a wavelength of 6.0 cm propagates along a string with speed of 4.0 m/s. What is the speed of a wave with two times shorter wavelength, 3.0 cm , propagating on the same string? O 2.0 m/s O 4.0 m/s O 8.0 m/s O Neither of the aboveTwo transverse sinusoidal waves combining in a string are described by the wave functions y1 = 0.02 sin(2Ttx+Ttt) and y2 = %3D 0.02 sin(2rtx-Tt), where x and y are in meters, and t is in seconds. If after superposition, a standing wave of 3 loops is formed, then the length of the string is: 0.5 m 1 m 2 m 0.75 m 1.5 mIf y(x,t) = ( 5.6 mm) sin[kx + ( 460 rad/s)t + q] describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = + 3.2 mm and y = - 3.2 mm?