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Using Waveform Equations The equation for a pulse travelling through a medium is given by D(x,t)=(3.0 m^3)/((x-(2.0 m/s)〖t)〗^2+5.0 m^2 ) Where x and D are in metres and t is in seconds. What is the speed of the pulse, and in which direction is it travelling? What is the displacement of a point of the medium located at x = 0.30 m at t = 1.0 s? What is the maximum displacement of a point as the pulse passes through it? Plot the displacement as a function of time of the point at x = 15.0 m as the pulse passes through it. What is the equation of a pulse that has the same velocity and shape as the above waveform but is inverted relative to it?
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Electrical Engineering
Transverse Displacement A pulse travelling through a string is described by the wave function D(x,t)=(2.0 m^3)/((x-(0.50 m/s)〖t)〗^2+ 4.0 m^2 ) Where x and D are in metres and t is in seconds. Find the velocity of the pulse. At t=2.0 s, what are the speeds of the string elements located at x=0.50 m and x=1.5 m? Graph the speed of the particle located at x=10.0 m between t=0.0 s and t=40.0 s.
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Electrical Engineering
Pulse Speed on a hanging String A string of linear mass density 20.0 g/m and length 10.0 m is hanging vertically from a high ceiling. A mass of 2.00 kg hangs freely from the lower end of the string. A pulse is generated at the lower end of the string and travels upward. What is the speed of the pulse at the lower end of the string, at the middle of the string, and at the top of the string?
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Electrical Engineering
Wave Speed and Wavelength The speed of sound waves is approximately 340 m/s in air and 1400 m/s in fresh water. What is the change in the wavelength of a sound wave of frequency 400 Hz when it crosses from air into water?
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Electrical Engineering
Travelling Harmonic Wave A harmonic wave travelling along a string is described by the wave function D(x,t)=(0.10 m)sin[(2.0 rad/m)x-(3.0 rad/s)t] Where x is in metres and t is in seconds. Determine the wavelength and the frequency of the wave What is the velocity of the wave? What is the displacement of the segment of the string located at x=0.30 m at t=1.0 s and at t=1.2 s? Determine the average speed of the segment during this time, and compare it to the wave speed Plot the displacement of the segment at x=0.3 m between t=1.0 s and t=5.0 s. Plot the shape of the section of the string between x=0.50 m andx=3.0 m at t=0.50 s and t=0.60 s.
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Electrical Engineering
Phase Constant of a Harmonic Wave A sinusoidal wave travelling in the positive x-direction has amplitude 0.15 m, wavelength 0.40 m, and frequency 8.0 Hz. The displacement at t = 0 of a point located at x = 0 is 0.15 m. What is the phase constant of the wave? Write an equation for the wave function of this wave.
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Electrical Engineering
A Harmonic Wave A harmonic wave on a string is described by the wave function D(x,t)=(0.20 m)sin((2.0 rad/m)x-(3.0 rad/s)t. What is the velocity at t=0.0 s of a segment of the string located at x=0.50 m? What is the maximum positive velocity of this segment? When is the first time after t=0.0 that the segment attains this velocity? Plot the segment’s velocity for 0.0 s≤t ≤10.0 s.
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Electrical Engineering
The Position Plot of a Harmonic Wave Suppose that the position plot in Figure 14-37 was obtained at t = 1.0 s and the wave is moving at a speed of 1.5 m/s toward increasing x. Determine the frequency and the phase constant for this wave, and write an equation for the wave function of this wave.
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Electrical Engineering
