# REPORT ON PLOTS OF PRESSURE AND VELOCITY ALONG THE LENGTH OF THE TUBE

## RESULTS OF THE TEST RIG USING MMM (MULTI MICROPHONE METHOD)

* The microphones are kept at axial locations as follows
$x_1$ = 220mm
$x_2$ = 380mm
$x_3$ = 510mm
$x_4$ = 620mm
$x_5$ = 700mm (all the distances are measured from the source i.e, speaker)

* The tube (test rig) is of length $1mm$

### PLOTS OF PRESSURE AND VELOCITY ALONG THE TUBE FOR FREQUENCY RANGE (250 Hz - 2500 Hz)

* The cutoff frequency of the tube for the first order modes = 1596Hz ($\phi=140mm$)
* the pressure and velocity distribution along the length of the tube are plotted for frequencies - $f = 250Hz, 500Hz, 800Hz, 1100Hz, 1400Hz, 1596Hz$ (cutoff frequency)
* for frequencies after cutoff frequency $f = 1900Hz, 2200Hz, 2500Hz$
* desired frequency range = $250Hz-2500Hz$

### WITH FOAM AT SPEAKER END

#### Chirp signal with amplitude 1mV, frequency from 250Hz-2500Hz and time 50sec

##### plot of pressure vs length of tube

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=250Hz-800Hz$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=800Hz-1596Hz$ (cutoff frequency)

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=1600Hz-2500Hz$

##### plot of velocity vs length of tube

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=250Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=500Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=800Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1100Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1400Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1596Hz$(cutoff frequency)

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1900Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2200Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2500Hz$

#### Chirp signal with amplitude 2mV, frequency from 250Hz-2500Hz and time 50sec

##### plot of pressure vs length of tube

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=250Hz-800Hz$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=800Hz-1596Hz$ (cutoff frequency)

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=1600Hz-2500Hz$

##### plot of velocity vs length of tube

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=250Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=500Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=800Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1100Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1400Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1596Hz$(cutoff frequency)

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1900Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2200Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2500Hz$

#### Chirp signal with amplitude 3mV, frequency from 250Hz-2500Hz and time 50sec

##### plot of pressure vs length of tube

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=250Hz-800Hz$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=800Hz-1596Hz$ (cutoff frequency)

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=1600Hz-2500Hz$

##### plot of velocity vs length of tube

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=250Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=500Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=800Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1100Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1400Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1596Hz$(cutoff frequency)

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1900Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2200Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2500Hz$

### WITH OUT FOAM AT SPEAKER END

#### Chirp signal with amplitude 1mV, frequency from 250Hz-2500Hz and time 50sec

##### plot of pressure vs length of tube

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=250Hz-800Hz$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=800Hz-1596Hz$ (cutoff frequency)

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=1600Hz-2500Hz$

##### plot of velocity vs length of tube

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=250Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=500Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=800Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1100Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1400Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1596Hz$(cutoff frequency)

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1900Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2200Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2500Hz$

#### Chirp signal with amplitude 2mV, frequency from 250Hz-2500Hz and time 50sec

##### plot of pressure vs length of tube

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=250Hz-800Hz$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=800Hz-1596Hz$ (cutoff frequency)

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=1600Hz-2500Hz$

##### plot of velocity vs length of tube

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=250Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=500Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=800Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1100Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1400Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1596Hz$(cutoff frequency)

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1900Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2200Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2500Hz$

#### Chirp signal with amplitude 3mV, frequency from 250Hz-2500Hz and time 50sec

##### plot of pressure vs length of tube

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=250Hz-800Hz$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=800Hz-1596Hz$ (cutoff frequency)

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=1600Hz-2500Hz$

##### plot of velocity vs length of tube

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=250Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=500Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=800Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1100Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1400Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1596Hz$(cutoff frequency)

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1900Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2200Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2500Hz$

#### Chirp signal with amplitude 4mV, frequency from 250Hz-2500Hz and time 50sec

##### plot of pressure vs length of tube

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=250Hz-800Hz$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=800Hz-1596Hz$ (cutoff frequency)

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequencies $f=1600Hz-2500Hz$

##### plot of velocity vs length of tube

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=250Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=500Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=800Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1100Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1400Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1596Hz$(cutoff frequency)

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=1900Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2200Hz$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ (with a step of $t=10sec$) and frequency $f=2500Hz$