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?

## Answer:

The speed of sound as measured by the Kundt's tube apparatus
is 2 times the distance between nodes times the frequency of the
oscillator, assuming that the oscillator puts out a single
frequency only and not some more complex waveform. The speed of
sound is related to the air pressure and temperature which does
not change in your experiment. So when you change the frequency
of the oscillator, the distance between the nodes in the tube
will change so as to give you the same result for sound speed.
The old d was 1/2 the old wave length. The new d is 1/2 the
new wavelength. If the wavelength was halved, then the new d is
1/2 the old d, not 1/4. The new d is 1/4 the old wavelength.

You are right about the powder being dry so it is free to
respond to the small pressure difference carried by the sound
wave.