Question

5: Wave on a hanging string (8 points) A heavy metallic cable of length L and mass m hangs from the ceiling. (a) (2 points) If we define the bottom of the cable to be where y = 0 and the ceiling to be y = L, what's the tension in the cable at a point y along the cable? (Hint: How much weight is it supporting?) (b) (2 points) What's the speed of a vibrational wave traveling along the cable at a point ? (c) (4 points) A wave starts at the top of the cable and travels to the bottom. What's the time it takes to reach the bottom? (Hint: The speed is variable, so you'll have to integrate dt, and ask yourself how dt is related to dy.)

Answer 1

ą Griven (1 . - m length of heavy metallic cable hangs from celling. is 2 and mass - FBD p y=L Consider a little piece at height y from the bottom and we drawn a free body diagram of Watle piece Now Efy = may where {fy = tatal mags in direction to ands ay = acceleration in ydirection 0 F-W = F w If = = 1 this is the cable. the tension at a point y along

6 Now the speed of a vibrational ware traveling along the cable at a point yas. where f = tension at paintyy . tag . We know that = dt = dugo Jeht = f d this is the the wave time takes to reach the bottom by