Experiment 1 - Part 3

Q1: Why is the Orgel equation used to estimate resonance frequency?

The Orgel equation is a simplified model based on an organ pipe analogy. It treats the pneumatic cavity like a resonating acoustic tube.
It gives a rough estimate of the first resonance frequency assuming:

• One open end and one closed end

• Uniform geometry and ideal conditions
  This provides a quick check for expected dynamic behavior, but it doesn’t include damping or real-world losses.

Q2: Why is the estimated 122.5 kHz resonance not visible in the FFT?

Several valid reasons:

• The sensor-cavity system acts like a low-pass filter, attenuating high frequencies.

• The shock wave energy may not excite the cavity at 122.5 kHz sufficiently.

• The data acquisition system’s effective bandwidth or sampling rate might limit detection of such high frequencies.

• Internal sensor design (membrane mass/damping) may suppress this resonance.

Q3: Why do we see low-frequency peaks around 150–200 Hz instead?

These likely come from:

• The shock wave’s broadband pressure jump, exciting natural modes of the system.

• Probe housing vibration or reflections.

• Interaction between the membrane and cavity structure, which often respond strongest to low frequencies.
  This is a common behavior in dynamic sensors designed for unsteady flows — they sacrifice high-frequency sensitivity to be more robust in the operating range.

Q4: What does the absence of high-frequency content imply for data processing?

It shows that the sensor behaves as a low-pass filter, which:

• Limits the ability to detect rapid fluctuations (e.g. blade passing events)

• May underestimate pressure spikes in real turbomachinery tests
  Therefore, correction functions, deconvolution, or dynamic calibration are needed during post-processing to recover the original signal shape.

Q5: How would you improve your FFT-based dynamic calibration in a future setup?

• Use shorter cavities → pushes resonance frequency higher.

• Improve sampling rate and resolution of the data acquisition system.

• Use a more energetic shock to excite higher modes.

• Place sensors closer to the wall to minimize signal distortion.

• Implement windowing and filtering before FFT to isolate clean sections of the signal.