# Pressure Tube Response Time

1. Oct 6, 2009

### Ron D

A high-frequency response pressure transducer at one end of a 7 inch long (approx. 0.6 inch ID) tube will be used to measure static pressure pulsations in a duct of flowing air. Interest is for air at 70 F and at 460 F. The transducer end of the measurement tube has no appreciable volume. What is the frequency response of the measurement system? In other words, what is the highest duct frequency that can be measured with reasonable engineering accuracy?

Are there references that outline the relevant acoustics theory?

Thanks. ....Ron

2. Oct 6, 2009

### FredGarvin

If you can wing it, it is always best to flush mount dynamic pressure transducers to the flowpath. However, if that is not possible, you will want to shorten the interface tube as much as possible. The Helmholtz resonator natural frequencies can be calculated from

$$f_n=\frac{c}{4 \pi} \left[\frac{\pi d^2}{V(L+.85d)} \right]^{.5}}$$

where
V= volume under sensing diaphragm
c = speed of sound
d = diameter of the tube
L = length of tube

If the volume of the tube can be reduced to about half of that of the resonator chamber, then the wave equation form can be used which is a bit simpler:

$$f_n = \frac{(2n-1)c}{4L}$$

3. Oct 6, 2009

### Ron D

First, a correction: The tube ID is about 0.06 inch, not 0.6 inch.