6-A uniform string is fixed at the ends x = 0 and x = (l) are fixed. One end is taken at the origin and at a distance 'b' from this end the string is displaced a distance 'h' transversely and is released from rest in that position. Find the displacement of any of the string at any subsequent time.
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- 10 Figure 17-30 shows a stretched string of length L and pipes a, b, c, and d of lengths L, 2L, L/2, and L/2, respectively. The string's tension is adjusted until the speed of waves on the string equals the speed of sound waves in the air. The fundamental mode of oscilla- tion is then set up on the string. In which pipe will the sound pro- duced by the string cause resonance, and what oscillation mode will that sound set up? L.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) n13: An infinite long string having one end x = 0 is initially at rest on the x-axis. The end x = 0 undergoes a periodic transverse displacement given by A, sinot, t>0. Find the displacement of any point on the string at any time.
- 7Current Attempt in Progress The function y(x, t) = (26.0 cm) cos(TX - 29xt), with x in meters and tin seconds, describes a wave on a taut string. What is the transverse speed for a point on the string at an instant when that point has the displacement y= +23.0 cm? Number i UnitsSubject:- Physics A string of mass m = 103 g is 3.2 m long. One end of it is attached to a wall, and the other end passes over a pully with a mass of 6.6 kg attached to the end of the hanging string. Ignore the mass of the hanging string for the tension calculation. . If the length of the horizontal portion of the string is 1.7 m, how long does a pulse take to travel the full length of the horizontal part of the string?
- 2#5Figure Q3(a) shows two different modes of one-dimensional chain of atoms vibrate by displacing from equilibrium positions horizontally (longitudinal) and vertically (transversal). Explain these modes. direction of travel displacement Figure Q3(a) Longitudinal (upper chain) and Transversal (lower chain) waves.
- Q6) A string of infinite length is stretched from -0 to +0 and subjected to the following initial velocity: 1 -1sx<0 v(x) ={-1 0sxsl 0 otherwise Find the initial displacement required to be applied in order the resulting motion will be: (a) Wave traveling to the right only (b) Wave traveling to the left only3 Organ Pipes In a pipe organ, air is forced to flow through hollow pipes with precisely determined lengths. One end of the pipe is always open, to allow air into the pipe. The other end may be opened or closed. (a) If a pipe is to generate a note with a frequency of 256 Hz (middle C) when closed at one end, how long should the pipe be? (b) What are the frequencies of the next two harmonics produced by this pipe? (These are the pitches of the next two standing waves that the pipe will admit.) (c) What fundamental frequency will the pipe produce if both ends are open? (d) What are the frequencies of the next two harmonics when both ends are open? (These are the pitches of the next two standing waves that the pipe will admit.) Draw a picture that shows the standing waves in each case. Upload it.90 A certain transverse sinu- soidal wave of wavelength 20 cm is moving in the positive direc- I (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 and x = 20 cm at t = 2.0 s. Figure 16-49 Problem 90. u (cm/s)