Vibrations and Waves Legacy Problem #21 Guided Solution

Like any problem, I need to approach this problem using the habits of an effective problem solver. I need to read the problem carefully and begin to visualize the physical situation, writing down the things that I know, the things that I'm looking for. I read here of a standing wave pattern that's been established in a snakey by vibrating it up and down 32 vibrations in 10 seconds. I write that down. That's important information. I'm told that Gerald is standing a distance of 6.2 meters from Mr. H as the standing wave pattern shows. So that's the distance from one end of the snakey to the other end of the snakey. And here's important information. There's four equal length sections in the snakey. Now as I read this, I begin to sketch a standing wave pattern. Simply a sine wave pattern as your math teacher would describe it. And then I shake it in such a manner that there's four equal length sections from one end to the other end, which is a 6.2 meter distance. What I'm calculating here is f for frequency, wavelength for lambda, and speed, or v. So my strategy is going to center around using the verbal information to get the frequency and the wavelength, and then using the wave equation to get the speed. So getting the frequency is a matter of taking the 32 vibrations in the 10 seconds and using it with the concept of frequency to find out. Frequency is the number of cycles per second, or 32 vibrations per 10 seconds. So if I divide 32 by 10, I'm getting the vibrational cycles per second. That would come out to be 3.2 vibrations per second, or cycles per second. 3.2 hertz, that's the frequency. Now this distance of 6.2 meters is a distance on the diagram I've drawn that goes from the one end to the other end. And there are four equal length sections there. Each equal length section is being equivalent to a half of a wavelength. So the 4 halves wavelength equals 6.2 meters. If I divide each side by 2, or by 4 halves, I'm going to get myself a wavelength, and it comes out to be 3.1 meters. So that's wavelength. Now I know frequency and I know wavelength, and if I multiply, I'll get the speed. That's the wave equation, speed equal frequency times wavelength. When I do that multiplication, I get 9.92 meters per second, and I can round that to two significant digits.