Question

A composite string is made up of a short length of heavy string (µ1) and a...

A composite string is made up of a short length of heavy string (µ1) and a very very long length of much lighter string (µ2 µ1). The light end of the string is attached to a pole very far away. The string is held under tension by passing the heavy end over a pulley and attaching it to a bag full of sand. The heavy segment of the string has length L (between the pulley and the knot between the two strings).

a) I pluck the end of the string by the pulley, launching an upright pulse that travels to the left starting on the heavy string. When the pulse encounters the knot between the light and heavy string, I see a transmitted and reflected pulse. Draw the reflected and transmitted pulses, clearly indicating any differences in: spatial size, amplitude, and polarization (upright or inverted).

b) I now excite the string sinusoidally in time by gently shaking the pulley up and down; the frequency I excite the string at is variable. I start at a very low frequency and slowly turn up the frequency. As I do this, I see standing waves appear on the heavy portion of the rope. I turn the frequency up until I have found the third such standing wave. Draw the pattern that this standing wave makes on the heavy rope.

c)I now leave the frequency of excitation fixed (the third standing wave is being excited) and then I cut a small hole in the bottom of the sand bag so that sand starts slowly trickling out, lowering the mass of the sand bag. At first, my exciting frequency goes out of resonance, and I do not see a standing wave on the heavy part of the string. After a short while later however, I see a new standing wave excited on the string. Draw this standing wave.

d)What is the fractional change in the mass of the sandbag at that instant (mnew/mold)?

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