A narrow, nearly massless string is stretched horizontally and joined to a second string of greater mass per unit length. The common tension in both strings is 35N. Measured properties are summarized below.
• Linear density of left-hand string (Region L): 1.0×10−3kgm−1
• Linear density of right-hand string (Region R): 4.0×10−3kgm−1
At time t=0, the center of a rectangular upward pulse of width 0.20m is located 0.50m to the left of the junction and moving toward it. Ignore dispersion so the pulse width remains constant in each region.
(a) Calculate the speeds vL and vR at which small transverse disturbances propagate in Regions L and R, respectively. Express each answer to two significant figures.
(b) Determine the position (measured from the original junction) of the center of the transmitted pulse at time t=12ms.
(c) Determine the position of the center of the reflected pulse at the same instant.
(d) On your answer sheet, sketch the strings at t=12ms. Clearly label the reflected and transmitted pulses, indicate their directions of motion, and show whether either pulse is inverted relative to the original disturbance.