Kundt's Tube Experiment

## Question:

Today, we have taught kundt's Tube experiment. In the this experiment, a stationary wave is set up inside a closed tube. Lycopodium powser is spread evenly inside the tube. The node positions of the stationary wave will form heaps on the powders. Distance d between two heaps is measured and the frequency of the wave is denoted as f.

It is said in our textbook that the speed of sound in air is given by c=2df. As in the experiment, we can change the frequency of the signal generator , thus changes the frequency of the wave. If I change the frequency, I know that the distance d will also change. But will they change in proportion? Will the final speed be different?

I have tried to prove this mathematically, and what I obtain is: AS f is proportional to 1/lambda when frequency f doubled, lambda prime becomes one half of lambda. And as lambda is proportional to 2d, when lambda prime becomes one half of lambda, d prime becomes 1/4 d. As v=2df, v prime = 2 (1/4 d)X(2f) = df , which is not equal to v !

Is there anything wrong in my calculations?

Also, I wonder why the tube has to be dry? is it beecause we want to avoid the powders from sticking together?