Vibrations and Waves Legacy Problem #11 Guided Solution

An effective problem solver will read a problem carefully and develop a mental picture of what's going on. An effective problem solver would begin to list known quantities and relate them to variables in typical physics equations. And a good problem solver will list unknown quantities and begin to plot out a strategy using understanding of concepts and formulas in order to go from the known quantities to the unknown quantities. Here we read of a transverse wave that's moving along a lengthy rope. When I read that statement, one of the first things I do is I draw a little wave pattern. I'm told adjacent crests are positioned 2.4 meters apart. I look on my wave pattern and I recognize that the distance from one of my crests to the next crest is 2.4 meters. I understand that to be the wavelength. So I list on my sheet of paper lambda equal 2.4 meters, where lambda is the wavelength. I'm told exactly six crests are observed to move past a given point along the medium in 9.1 seconds. So in my pattern, I picture a point, any point on that pattern, and I'm thinking this wave is moving along, traveling along, and six of these crests are moving past a point in 9.1 seconds. What that's information about is that's information about finding the period. It's not the period because my conceptual understanding tells me the period is the time for one wave cycle to move past a point, and here I have six wave cycles moving past a point in 9.1 seconds. So that 9.1 seconds is equal to six time periods. So if I want to find the period, I'm going to list t equal 9.1 seconds divided by six. Now what I'm looking for, my unknowns, are the wavelength, which I've already determined, the frequency, which I'll need to determine, and the speed, which I'll need to determine. So to find the frequency from the period and the wavelength, I can figure that the frequency is simply the reciprocal of the period. So I can take the 9.1 seconds and divide it by six. That gives me the period. And then I can take the reciprocal of that, and that will give me the frequency. The period comes out to be 1.5167, and when I take the reciprocal of this, I get 0.6593 hertz, and I can round that to two decimal places. Now to calculate the speed, I need to use the so-called wave equation, v equal f times lambda. The f part I've just calculated, the 0.6593 hertz, and the lambda is 2.4 meters. So if I multiply these two quantities together, I get 1.5824 meters per second, and I can round that to two significant digits.