# Standing Wave with an Unexpected Pressure Field

Recently, I have tried to measure pressure in a '' Standing Wave (SW)'' field established in air using a 1/8'' traversing microphone (B&K). The ''SW'' field (at 60kHz) is produced using a circular electrostatic broadband transducer (34 mm in diameter) flushed-mounted at the side wall of a rectangular channel. The frequency of the transducer is set to match a full wavelength between transducer and a parallel reflector made of Aluminium.

To measure the pressure, the microphone is inserted through an approx. 1/8'' hole in the reflector exactly at the centre of the transducer. The pressure signal is acquired at increment size of 50$\mu$m from the reflector to the transducer face using a LabView card with 1MHz sampling frequency over a 4s timespan. The attached figure shows the result of this experiment where the RMS of the pressure fluctuation (P$_{RMS}$) is plotted against the relative distance from the transducer.

It is expected that the microphone itself perturbs the field therefore, if we only consider the first point where the microphone was flush-mount in the reflector, why do not we see a pressure anti-node at the wall?

The wavelength you describe trying to measure, $$\lambda = \frac cf = \frac{330 \rm\,m/s}{60\rm\,kHz} = 5.5\rm\,mm$$ is quite short compared to "typical" sound wavelengths; that particular frequency is far above the $20\rm\,kHz$ cutoff of what's audible to humans.
You don't say what the transverse dimensions of your rectangular channel are, but the fact that you have a $\frac 18'' = 3\rm\,mm$ microphone in the channel suggests that it is wide compared to the wavelength of the sound that you are trying to measure. In that case, the approximation that the waveguide is supporting sound propagation in one dimension is poor, and a substantial fraction of the sound power can be carried in modes which are transverse to the "long" dimension of your guide. At the center of the guide you might have a node in the pressure due to the longitudinal propagation of the sound, but an antinode due to the transverse modes. Since your pressure sensor is ignorant of direction, deconvolving these would be complicated.