#$&*
phy 232
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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First Question: At clock time t the left-hand end of a long string undergoes SHM in the y direction, with amplitude .62 cm and angular frequency 3 `pi rad/s. Give a possible equation for the motion of this end. The motion of this end creates a traveling wave in the string.
The string extends along the x axis, with the origin at the left end of the string, which is held under tension 17 Newtons and has mass per unit length 5 grams / meter.
• Find the equation for the y displacement a point 19.4 meters down the string as a function of clock time.
• If the position of the left-hand side is x = 0, find the equation for the y displacement as a function of clock time at arbitrary position x.
• University Physics: Show that your equation satisfies the wave equation.
Give and graph the equation for the shape of the string at clock time t = .083 sec.
Second Question:
A string is under a tension of 15 Newtons and lies along the x axis. Beads with mass 4.7 grams are located at a spacing of 5 cm along a light but strong string. At t = 0 bead A is moving in the y direction at .0301 m/s, and this bead is at at y position .002 meters, while the bead to its right is at y position .0015 meters and the bead to its left at y position .0015 meters. Find:
• the acceleration of the given bead
• its approximate velocity .02 seconds later and
• the distance it will move in the .02 seconds.
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ok for the first question I understand that you need to use y=Asin(Wt) or the single harmonics motion equation, but what I do not understand is how you are supposed to plug in an x distance into it. I tried plugging in length/velocity because that would equal seconds but then my equation got too crazy. And how do you show that the SHM equation solves the wave equation? Then after that I do not understand where to take it from there, can you help me with it or point me in the right direction.
The time delay between the left end and position x relative to the left end is x / c, where c is the speed of propagation. Thus y = A sin( omega ( t - x / v) ). What happens at position x is what happened previously at the left end, where 'previously' means the time which is x / v earlier. Check also the Introductory Problem Sets.
The wave equation relates the second partial derivative of the wave function with respect to x to the second partial derivative with respect to t. Look up 'wave equation' in the index of your book.
And for the second question I know that we did this in a lab but how do you do this with only the positions of the beads? I feel like not enough information is given here.
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Thank you
See my note on the first question.
The second was inadvertently left out of the materials so you don't need to worry about it.