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sapiental

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Hello,

I have a couple of questions about my assignment. Here are the assigned questions plus my attempts.

1) One end of a rope is tied to a stationary support at the top of a

vertical mine shaft 80.0 m deep. The rope is stretched taut by a box of mineral samples with a mass of 20.0 kg attached at the lower end. The mass of the rope is 4.00 kg. The geologist at the bottom of the mine shaft signals a colleague at the top by jerking the bottom of the rope

sideways. How long does it take for the wave pulse to arrive at the top of the 80.0 m long rope?

For transverve waves v = sqrt(F/u) u = mass per unit L

F = mass_rope + mass_box (g)

F = 24.0kg (9.8m/s^2)

v = sqrt(325N/.05kg/m)

v = 80.6m/s

so it would take about 1 second for the wave pulse to arive

2) Motion of a Wave Pulse :

If the end of a string is given a single shake, a wave pulse

propagates down the string. A particular wave pulse is described by the function:

y(x,t) = (A^3/(A^2 + (x - vt)^2))where A = 1.00 cm, and v = 20.0 m/s.

a) Sketch the pulse as a function of x at t = 0. How far along the string does the pulse

extend?

I used MATLAB for this but don't know if I did it correctly. Since t = 0 the equation becomes:

y(x, t = 0) = (A^3/(A^2 + (x - v(0))^2))

i used the command plot(x,y) I let x = 0 through 1

plot(x, (.01m^3/(.01m^2 + (x)^2)

If my plot is correct it looks like the pulse extends roughly .16m.

Should my sketch look like a wave? Because mine just looks like one curve..

b) Sketch the pulse as a function of x at t = 0.001 s.

I attached a picture of my graph but I basically used the function plot(x, (.01m^3/(.01m^2 + (x - 20m/s * .001s)^2)

c) At the point x = 4.50 cm, at what time t is the displacement maximum?

Well I think I messed up on the graphs at this point because one axis is time and my y axis is x.. If anyone could tell me how I should go about graphing this function It would be much appreciated.

d) At which two times is the displacement at x = 4.50 cm equal to half its maximum value?

e) Show that y(x, t) satisfies the wave equation.

I roughly undertand the wave equation and I can recognize that this equation posesses similar properties. But I don't know what my first step should be. Maybe partially differentiate either the wave function or this particular function?

Thanks any help is much appreciated.

I have a couple of questions about my assignment. Here are the assigned questions plus my attempts.

1) One end of a rope is tied to a stationary support at the top of a

vertical mine shaft 80.0 m deep. The rope is stretched taut by a box of mineral samples with a mass of 20.0 kg attached at the lower end. The mass of the rope is 4.00 kg. The geologist at the bottom of the mine shaft signals a colleague at the top by jerking the bottom of the rope

sideways. How long does it take for the wave pulse to arrive at the top of the 80.0 m long rope?

For transverve waves v = sqrt(F/u) u = mass per unit L

F = mass_rope + mass_box (g)

F = 24.0kg (9.8m/s^2)

v = sqrt(325N/.05kg/m)

v = 80.6m/s

so it would take about 1 second for the wave pulse to arive

2) Motion of a Wave Pulse :

If the end of a string is given a single shake, a wave pulse

propagates down the string. A particular wave pulse is described by the function:

y(x,t) = (A^3/(A^2 + (x - vt)^2))where A = 1.00 cm, and v = 20.0 m/s.

a) Sketch the pulse as a function of x at t = 0. How far along the string does the pulse

extend?

I used MATLAB for this but don't know if I did it correctly. Since t = 0 the equation becomes:

y(x, t = 0) = (A^3/(A^2 + (x - v(0))^2))

i used the command plot(x,y) I let x = 0 through 1

plot(x, (.01m^3/(.01m^2 + (x)^2)

If my plot is correct it looks like the pulse extends roughly .16m.

Should my sketch look like a wave? Because mine just looks like one curve..

b) Sketch the pulse as a function of x at t = 0.001 s.

I attached a picture of my graph but I basically used the function plot(x, (.01m^3/(.01m^2 + (x - 20m/s * .001s)^2)

c) At the point x = 4.50 cm, at what time t is the displacement maximum?

Well I think I messed up on the graphs at this point because one axis is time and my y axis is x.. If anyone could tell me how I should go about graphing this function It would be much appreciated.

d) At which two times is the displacement at x = 4.50 cm equal to half its maximum value?

e) Show that y(x, t) satisfies the wave equation.

I roughly undertand the wave equation and I can recognize that this equation posesses similar properties. But I don't know what my first step should be. Maybe partially differentiate either the wave function or this particular function?

Thanks any help is much appreciated.

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