Vibrations and Waves Legacy Problem #20 Guided Solution

This problem centers around the analysis of a diagram of a standing wave pattern and a verbal statement which gives us a frequency and a length of the chord which is used to create the standing wave pattern. We're told that the distance from one end to the other end of this chord is 1.38 meters and it begins vibrating as shown in the pattern. If we look at that vibration, we'll notice that that's the so-called fifth harmonic frequency or the fifth harmonic standing wave pattern. The distance from one end to the other end of 1.38 meters is equivalent to five-halves of a wavelength. The way I figured five-halves of a wavelength is that I know that the distance from rest up to a high point back down to a rest is equal to half a wavelength. Same distance from rest down to the low point back up to rest is equal to half of a wavelength. So from end to end there's five of these distances and so 1.38 meters is equal to five-halves of a wavelength or 2.5 wavelengths. I write that equation down as such and then I divide by 2.5 and when I do I get the wavelength value and it comes out to be 0.55200 meters. Now that's the wavelength but what I'm looking for is the speed and I understand that the wave equation is v equal f times lambda where v is the speed, what I'm looking for in this problem, f is the frequency given here is 79.4 hertz and lambda is the wavelength which I've just calculated. So if I take my 79.4 hertz and I multiply it by 0.552 meters I'll get the speed and it comes out to be 43.8288 meters per second and I can round that to three significant digits.