A1.50-m string of weight 0.0125 n is tied to the ceiling at its upper end, and the lower end supports a weight w. ignore the very small variation in tension along the length of the string that is produced by the weight of the string. when you pluck the string slightly, the waves traveling up the string obey the equation: y(x, t) = (8.50 mm)cos(172 rad/m x − 4830 rad/s t)assume that the tension of the string is constant and equal to w. (a) how much time does it take a pulse to travel the fulllength of the string? (b) what is the weight w? (c) how many wavelengths are on the string at any instant of time? (d) what is the equation for waves traveling down the string?

Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. so it is no surprise that such clothing has largely replaced thickand heavy old-fashioned coats. (a) consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 w/m·°c) with 1.5-mm-thick air space (k = 0.026 w/m·°c) between the layers. assuming the inner surface temperature of the jacket to be 28°c and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°c and the heat transfer coefficient at the outer surface is 25 w/m2·°c. (b) what would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? what should be the thickness of a wool fabric (k = 0.035 w/m·°c) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a five-layer ski jacket?