Gradient of Wavelength vs Period Graph?

[donkeycopter]

We've got a table of periods (in seconds) and their corresponding wavelengths for creating resonance in a closed pipe.

I've been told that plotting a graph of period (on x axis) vs wavelength, and finding the gradient of that linear line will tell me the speed of sound in air. I can do that easily and found the speed in air to be 375m/s - which is reasonable.

I want to know why this works though. Why do I plot a graph of wavelength against period? Why is the gradient the speed of sound in air?

I'm assuming it is something to do with the linear equation (y=mx + c) relating the the universal wave equation (v = f x lambda). And f being inversely proportional to the period (T). But i have no idea how they relate!

An in-depth explanation would be amazing! I can do the question easily, I always just want to know why what we've been told to do works :)

 

[rl.bhat]

Your assumption is correct. You know that

v = f*λ. So

λ = v/f. Bur 1/f = T. So

λ = v*T => y = mx.

The slope of the graph is the velocity.