Problem 1: Pulse on a rope The rope of the length 6 m is fixed to...
A heavy rope with length L and mass M is attached to the ceiling and is allowed to hang freely. (a) Find an expression for the tension in the rope at a point a distance y from the bottom, and use this to show that the speed of transverse waves on the rope is independent of its mass and length but does depend on the distance y according to the equation ?=??. (b) If L = 3.0 m and the...
1. Travelling Waves A transverse wave travels along the length of a rope. The vertical displacement of any mass element of the rope is given by the function y(x.t) - 2sin(x+t+) in units of centimeters. Answer the following: () What is the velocity of the wave itself (indicate direction of motion as well)? (ii) Find the maximum transverse acceleration of the rope.
A pulse is sent traveling along a rope under a tension of 33 N whose mass per unit length abruptly changes, from 19 kg/m to 44 kg/m. The length of the rope is 3.0 m for the first section and 2.5 m for the second, and the second rope is rigidly fixed to a wall. Two pulses will eventually be detected at the origin: the pulse that was reflected from the medium discontinuity and the pulse that was originally transmitted,...
A traveling sinusoidal wave is moving on a long thin rope (total length =186 m, mass = 3.50 kg) in the +x direction. The rope is tied at one end to give a tension T. The wave is described by wavelength λ= 2.00 m, amplitude A=1.20 m and speed v=30.0 m/s. The phase angle is -π/4 radian. a. the expression that describes the y-displacement of the media particles as a function of time (give numbers for all the quantities). b. the...
A rope is fixed at both ends and under a tension of 100 N (where N is the symbol for newton, transverse displacement of the rope, in metres, is given by y = (0.5) sin ( x) cos | 4 1 + 100) t where x is distance along the rope in metres, x = 0 at one end of the rope, t is time in seconds, and N 17 (a) What are (i) the length of the rope, (ii...
In the game of tetherball a rope with length L = 1.40 m connects a ball with mass m = 0.500 kg to the top of a vertical pole so that the ball can spin around the pole as shown in the figure. L 0 What is the speed v of the ball as it rotates around the pole when the angle 0 of the rope is 34.0° with the vertical? m U = 1.917 m/s Incorrect
4. Travelling Waves and Their Characteristics A sinusoidal rope wave travels along the positive x - direction. You are also told that the speed of the wave is 20 cm/s, its frequency is 40 Hz, and that the wave is subject to the following initial conditions: at x = 0 and t = 0: y = +5 cm, and, at x = 0 and t = 0:09 = +10 cm/s (this is the transverse velocity of a point on the...
Consider a thin rope of mass m and length that hangs vertically from a fixed point at the top. Let the position of the lower end be and the top be . Because the rope is massive the tension will vary as a function of y. Show that the wave speed for this rope is and the time required for a wave to travel the whole rope is . We were unable to transcribe this imagey=0 We were unable to...
Problem 1 [8 pts] A uniform string of mass m and length L hangs vertically from the ceiling. (a) Find the tension in the rope as a function of distance from the lower end, and therefore determine the speed of a wave pulse as a function of position. (b) Solve by integration 2 = v(y) to determine the time it takes a wave pulse to travel the full length of the string.
Putting Everything Together (Exam-Type Question): A very wavy rope (2 pts). A person with a very nice hat shakes a long rope to make a transverse traveling wave as shown. The graph on the right is a zoomed-in snapshot of the beginning of the rope at time 0. The waveform travels down the rope to the right at a speed of v 1.8 m/s. Even though the wave is a little bit irregular, we will approximate it as a sinusoid....