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sapiental

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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?

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

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

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.

a) 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 (this is MATLAB a simple graphing program)

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

(Please see my attached graph a)

b) y(x, t = .001) = (A^3/(A^2 + (x - vt)^2))

Please see my attached graph1

c) y(x = .045m, t) = (A^3/(A^2 + (x - vt)^2))

I want to graph this as a function of t( t being the x axis) what range should I use for t ( i.e 1s, 2s..)?

My attempt is to let t = 0:.1:1 making the x-axis values (0s, .1s, .2s, ... 1s)

so to plot t vs (A^3/(A^2 + (x - vt)^2))

d) Can someone give me an iedea of how to graph the equation to get the actual wave on mt graph?

e) I think I have to take the partial derivative of either the wave equation or this particular pulse equation but I'm very bad at calc and havn't covered partial derivatives. If somebody could do this out for me step by step I would really learn alot.

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?

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

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

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.

a) 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 (this is MATLAB a simple graphing program)

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

(Please see my attached graph a)

b) y(x, t = .001) = (A^3/(A^2 + (x - vt)^2))

Please see my attached graph1

c) y(x = .045m, t) = (A^3/(A^2 + (x - vt)^2))

I want to graph this as a function of t( t being the x axis) what range should I use for t ( i.e 1s, 2s..)?

My attempt is to let t = 0:.1:1 making the x-axis values (0s, .1s, .2s, ... 1s)

so to plot t vs (A^3/(A^2 + (x - vt)^2))

d) Can someone give me an iedea of how to graph the equation to get the actual wave on mt graph?

e) I think I have to take the partial derivative of either the wave equation or this particular pulse equation but I'm very bad at calc and havn't covered partial derivatives. If somebody could do this out for me step by step I would really learn alot.