A string, fixed at both ends and 2.14 m long, is vibrating in its second harmonic. It excites a 0.5-m long pipe closed on one end into its third harmonic (first overtone). Use a speed of sound in air of 345 m/s if needed. (a) Sketch the normal modes given above for both the string and the closed-open pipe. [8] (b) What is the wave speed on the string? [7] (c) Write down the wave function y(x, t) for the 2nd harmonic wave on the string. Assume an arbitrary amplitude. [10] (d) If the mass density of the string is 0.55 g/m, what is the tension in the string? [5]

Copper has free electrons per cubic meter. a 71.0-cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 a of current. (a) how much time does it take for an electron to travel the length of the wire? (b) repeat part (a) for 6-gauge copper wire (diameter 4.12 mm) of the same length that carries the same current. (c) generally speaking, how does changing the diameter of a wire that carries a given amount of current affect the drift velocity of the electrons in the wire?

The focal length of a relaxed human eye is approximately 1.7 cm. when we focus our eyes on a close up object, we can change the refractive power of the eye by about 16 diopters. (a) does the refractive power of our eyes increase or decrease by 16 diopters when we focus closely? explain. (b) calculate the focal length of the eye when we focus closely.

Utah's great salt lake has an average salinity seven times higher than that of the oceans. very few multicellular organisms live in this harsh environment. an example is the brine shrimp, which must devote a large portion of its metabolic energy to osmoregulation. these brine shrimp must available hint(s)utah's great salt lake has an average salinity seven times higher than that of the oceans. very few multicellular organisms live in this harsh environment. an example is the brine shrimp, which must devote a large portion of its metabolic energy to osmoregulation. these brine shrimp must pump water back into their cells to counter its loss due to osmosisactively pump water back out of their cells to counter its inflow due to osmosissynthesize membranes that are impermeable to substances that upset osmotic balanceactively pump salt back out of their cells to counter its inflow due to osmosis