13: An infinite long string having one end x = 0 is initially at rest on the x-axis. The end x = 0 %3D undergoes a periodic transverse displacement given by A, sinot, t>0. Find the displacement of any point on the string at any time.
Q: What is the displacement Δx of the particle?
A: Approach to solving the question: Detailed explanation:Examples: Key references:
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Q: What is the displacement Δx of the particle?
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A: Simple problem from wave in a string. Please have a good look
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- In the normal mode of a vibrating string, multiple frequencies are present and one of these is the fundamental frequency of oscillation. The other frequencies present are called: harmonics; The answer cannot be found in the other choices. octaves; overtones;2. The displacements of a particle on a vibrating string as a periodic function of time t can be modeled for one cycle as s (t) = 10 + 114 sin (2πt), 0≤ t ≤ 1. Displacement units are cm, time units are seconds. (a) Find the velocity v (t) and acceleration a (t) of the particle. (b) At time t = 1/3, find the velocity and acceleration. Include the units of measurement in your answer. Is the particle moving left or moving right? Is the particle speeding up or slowing down? Provide your reasoning. (c) Determine the maximum speed of the particle. Verify your answer.90 A certain transverse sinu- soidal wave of wavelength 20 cm is moving in the positive direc- t (s) tion of an x axis. The transverse velocity of the particle at x = 0 as a function of time is shown in Fig. 16-49, where the scale of the vertical axis is set by u, = 5.0 cm/s. What are the (a) wave speed, (b) amplitude, and (c) frequency? (d) Sketch the wave between x = 0 andx = 20 cm at t = 2.0 s. Figure 16-49 Problem 90. (s/uɔ) n
- A stretched string of length L is fixed at both ends. It is plucked halfway along its length by producing an initial displacement h and then releasing the string. The expression for the string displacement at time t=0 is given by Select one: a. y(x, 0) = 4hx/L ob. O C. ≈ 4h(L-x)/L y(x, 0) = 2hx/L = 2h(L-x)/L y(x, 0) = 3hx/2L ≈ 3h (L-x)/2L d. y(x, 0) = 4hx/L ≈ 4h(L-x)/L 0#54. A travelling wave on a string is given by: = 5.7(cos(3.3x) cos(4.4t) – sin(3.3x) sin(4.4t)) y = For this wave find (a) its velocity of propagation (b) the transverse velocity (c) the transverse acceleration (d) the maximum displacement, velocity and acceleration of a particle on the string.