When the tube is in resonance, there is a displacement node at the
water, and a displacement antinode at the open end. This means there is
a pressure antinode at the water and pressure node at the open end.
The microphone measures pressure. If the microphone were "properly
placed" at the open end, the microphone output would be zilch during
resonance. I say "properly placed" because the location of the "end of
the tube" is not right at the physical end of the tube. During
resonance the displacement-antinode/pressure-node occurs beyond the
physical end of the tube by a distance approximately equal to the tube
radius. This is why, for accurate wavelength determination, you do not
want to measure from the end of the tube to the water level. What you
want to do is let water out until you hit the first resonance. Mark
this spot. Then let more water out until you hit the second resonance,
and mark this spot. The distance between the two water levels is
one-half wavelength. This is way more accurate than measuring from the
water to the end of the tube.
Once you have found the wavelength, take one-fourth and measure that
amount from the first resonance water level up toward the top of the
tube. You will find that the measurement puts you beyond the end of the
tube by about one radius.
Since your microphone is giving a signal when you hear the loudest
resonance, I assume your microphone is very near the end of the tube,
and is actually lower than the effective end of the tube. So when you
hear the resonance, the pressure node is above the microphone...
probably about 1 cm. Hence, when you lower the water by 1 cm the
pressure node moves downward about 1 cm, yielding the zero microphone
response that you observe.
If you should want to measure phase between the microphone and speaker,
use the oscilloscope in XY mode, put the speaker signal on X and the
microphone signal on Y.
We have students listen by ear for the loudest sound and don't usually
use a microphone. But sometimes we use a microphone, and when we do, we
observe the shape of the XY trace on the screen when we are near
resonance, and we mark that water level. Then we lower the water level
to the next resonance point and fine tune the XY trace to look the same
as when we made the first mark. We mark that water level as the second
resonance level. When done this way the distance between the marks is
quite accurately one-half wave.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu