# REPORT ON THE ERROR IN PRESSURE AND VELOCITY ALONG FREQUENCY RANGE FOR EACH MICROPHONE

## 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 ON ERROR IN PRESSURE AND VELOCITY ALONG FREQUENCY RANGE

* the error in pressure and velocity is plotted for the frequency range ($f=250Hz-2500Hz$)
* in all cases percentage error in pressure and velocity is plotted for the frequency range
* the predicted value of pressure and velocity are also plotted for the frequency range
($f=250Hz-2500Hz$) and time ($t=10,30,50sec$)
* the pressure and velocity are calculated using
- Pressure $$ P(f) = P_+(f)exp(-ikx) + P_-(f)exp(ikx) $$
- where $P_+(f)$ and $P_-(f)$ = pressure amplitudes of incident and reflected waves
- Velocity $$ U(f) = U_+(f)exp(-ikx) - U_-(f)exp(ikx) $$
- where $U_+(f)$ and $U_-(f)$ = pressure amplitudes of incident and reflected waves
$$U_+(f) = \frac{P_+(f)}{\rho_0c_0}$$$$U_-(f) = \frac{P_-(f)}{\rho_0c_0}$$
- where $\rho_0$ = density of medium (air)
$c_0$ = speed of sound in medium (air)
* desired frequency range = $250Hz-2500Hz$

### WITH FOAM AT SPEAKER END

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

##### plot of error and predicted pressure vs frequency range

##### mic1

* the plot of predicted pressure along frequency range for mic1

* the plot of error in pressure along frequency range for mic1

##### mic2

* the plot of predicted pressure along frequency range for mic2

* the plot of error in pressure along frequency range for mic2

##### mic3

* the plot of predicted pressure along frequency range for mic3

* the plot of error in pressure along frequency range for mic3

##### mic4

* the plot of predicted pressure along frequency range for mic4

* the plot of error in pressure along frequency range for mic4

##### mic5

* the plot of predicted pressure along frequency range for mic5

* the plot of error in pressure along frequency range for mic5

##### plot of error and predicted velocity vs frequency range

##### mic1

* the plot of predicted velocity along frequency range for mic1 (t=10sec)

* the plot of error in velocity along frequency range for mic1 (t=10sec)

* the plot of predicted velocity along frequency range for mic1 (t=30sec)

* the plot of error in velocity along frequency range for mic1 (t=30sec)

* the plot of predicted velocity along frequency range for mic1 (t=50sec)

* the plot of error in velocity along frequency range for mic1 (t=50sec)

##### mic2

* the plot of predicted velocity along frequency range for mic2 (t=10sec)

* the plot of error in velocity along frequency range for mic2 (t=10sec)

* the plot of predicted velocity along frequency range for mic2 (t=30sec)

* the plot of error in velocity along frequency range for mic2 (t=30sec)

* the plot of predicted velocity along frequency range for mic2 (t=50sec)

* the plot of error in velocity along frequency range for mic2 (t=50sec)

##### mic3

* the plot of predicted velocity along frequency range for mic3 (t=10sec)

* the plot of error in velocity along frequency range for mic3 (t=10sec)

* the plot of predicted velocity along frequency range for mic3 (t=30sec)

* the plot of error in velocity along frequency range for mic3 (t=30sec)

* the plot of predicted velocity along frequency range for mic3 (t=50sec)

* the plot of error in velocity along frequency range for mic3 (t=50sec)

##### mic4

* the plot of predicted velocity along frequency range for mic4 (t=10sec)

* the plot of error in velocity along frequency range for mic4 (t=10sec)

* the plot of predicted velocity along frequency range for mic4 (t=30sec)

* the plot of error in velocity along frequency range for mic4 (t=30sec)

* the plot of predicted velocity along frequency range for mic4 (t=50sec)

* the plot of error in velocity along frequency range for mic4 (t=50sec)

##### mic5

* the plot of predicted velocity along frequency range for mic5 (t=10sec)

* the plot of error in velocity along frequency range for mic5 (t=10sec)

* the plot of predicted velocity along frequency range for mic5 (t=30sec)

* the plot of error in velocity along frequency range for mic5 (t=30sec)

* the plot of predicted velocity along frequency range for mic5 (t=50sec)

* the plot of error in velocity along frequency range for mic5 (t=50sec)

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

##### plot of error and predicted pressure vs frequency range

##### mic1

* the plot of predicted pressure along frequency range for mic1

* the plot of error in pressure along frequency range for mic1

##### mic2

* the plot of predicted pressure along frequency range for mic2

* the plot of error in pressure along frequency range for mic2

##### mic3

* the plot of predicted pressure along frequency range for mic3

* the plot of error in pressure along frequency range for mic3

##### mic4

* the plot of predicted pressure along frequency range for mic4

* the plot of error in pressure along frequency range for mic4

##### mic5

* the plot of predicted pressure along frequency range for mic5

* the plot of error in pressure along frequency range for mic5

##### plot of error and predicted velocity vs frequency range

##### mic1

* the plot of predicted velocity along frequency range for mic1 (t=10sec)

* the plot of error in velocity along frequency range for mic1 (t=10sec)

* the plot of predicted velocity along frequency range for mic1 (t=30sec)

* the plot of error in velocity along frequency range for mic1 (t=30sec)

* the plot of predicted velocity along frequency range for mic1 (t=50sec)

* the plot of error in velocity along frequency range for mic1 (t=50sec)

##### mic2

* the plot of predicted velocity along frequency range for mic2 (t=10sec)

* the plot of error in velocity along frequency range for mic2 (t=10sec)

* the plot of predicted velocity along frequency range for mic2 (t=30sec)

* the plot of error in velocity along frequency range for mic2 (t=30sec)

* the plot of predicted velocity along frequency range for mic2 (t=50sec)

* the plot of error in velocity along frequency range for mic2 (t=50sec)

##### mic3

* the plot of predicted velocity along frequency range for mic3 (t=10sec)

* the plot of error in velocity along frequency range for mic3 (t=10sec)

* the plot of predicted velocity along frequency range for mic3 (t=30sec)

* the plot of error in velocity along frequency range for mic3 (t=30sec)

* the plot of predicted velocity along frequency range for mic3 (t=50sec)

* the plot of error in velocity along frequency range for mic3 (t=50sec)

##### mic4

* the plot of predicted velocity along frequency range for mic4 (t=10sec)

* the plot of error in velocity along frequency range for mic4 (t=10sec)

* the plot of predicted velocity along frequency range for mic4 (t=30sec)

* the plot of error in velocity along frequency range for mic4 (t=30sec)

* the plot of predicted velocity along frequency range for mic4 (t=50sec)

* the plot of error in velocity along frequency range for mic4 (t=50sec)

##### mic5

* the plot of predicted velocity along frequency range for mic5 (t=10sec)

* the plot of error in velocity along frequency range for mic5 (t=10sec)

* the plot of predicted velocity along frequency range for mic5 (t=30sec)

* the plot of error in velocity along frequency range for mic5 (t=30sec)

* the plot of predicted velocity along frequency range for mic5 (t=50sec)

* the plot of error in velocity along frequency range for mic5 (t=50sec)

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

##### plot of error and predicted pressure vs frequency range

##### mic1

* the plot of predicted pressure along frequency range for mic1

* the plot of error in pressure along frequency range for mic1

##### mic2

* the plot of predicted pressure along frequency range for mic2

* the plot of error in pressure along frequency range for mic2

##### mic3

* the plot of predicted pressure along frequency range for mic3

* the plot of error in pressure along frequency range for mic3

##### mic4

* the plot of predicted pressure along frequency range for mic4

* the plot of error in pressure along frequency range for mic4

##### mic5

* the plot of predicted pressure along frequency range for mic5

* the plot of error in pressure along frequency range for mic5

##### plot of error and predicted velocity vs frequency range

##### mic1

* the plot of predicted velocity along frequency range for mic1 (t=10sec)

* the plot of error in velocity along frequency range for mic1 (t=10sec)

* the plot of predicted velocity along frequency range for mic1 (t=30sec)

* the plot of error in velocity along frequency range for mic1 (t=30sec)

* the plot of predicted velocity along frequency range for mic1 (t=50sec)

* the plot of error in velocity along frequency range for mic1 (t=50sec)

##### mic2

* the plot of predicted velocity along frequency range for mic2 (t=10sec)

* the plot of error in velocity along frequency range for mic2 (t=10sec)

* the plot of predicted velocity along frequency range for mic2 (t=30sec)

* the plot of error in velocity along frequency range for mic2 (t=30sec)

* the plot of predicted velocity along frequency range for mic2 (t=50sec)

* the plot of error in velocity along frequency range for mic2 (t=50sec)

##### mic3

* the plot of predicted velocity along frequency range for mic3 (t=10sec)

* the plot of error in velocity along frequency range for mic3 (t=10sec)

* the plot of predicted velocity along frequency range for mic3 (t=30sec)

* the plot of error in velocity along frequency range for mic3 (t=30sec)

* the plot of predicted velocity along frequency range for mic3 (t=50sec)

* the plot of error in velocity along frequency range for mic3 (t=50sec)

##### mic4

* the plot of predicted velocity along frequency range for mic4 (t=10sec)

* the plot of error in velocity along frequency range for mic4 (t=10sec)

* the plot of predicted velocity along frequency range for mic4 (t=30sec)

* the plot of error in velocity along frequency range for mic4 (t=30sec)

* the plot of predicted velocity along frequency range for mic4 (t=50sec)
* 

* the plot of error in velocity along frequency range for mic4 (t=50sec)

##### mic5

* the plot of predicted velocity along frequency range for mic5 (t=10sec)

* the plot of error in velocity along frequency range for mic5 (t=10sec)

* the plot of predicted velocity along frequency range for mic5 (t=30sec)

* the plot of error in velocity along frequency range for mic5 (t=30sec)

* the plot of predicted velocity along frequency range for mic5 (t=50sec)

* the plot of error in velocity along frequency range for mic5 (t=50sec)

### WITH OUT FOAM AT SPEAKER END

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

##### plot of error and predicted pressure vs frequency range

##### mic1

* the plot of predicted pressure along frequency range for mic1

* the plot of error in pressure along frequency range for mic1

##### mic2

* the plot of predicted pressure along frequency range for mic2

* the plot of error in pressure along frequency range for mic2

##### mic3

* the plot of predicted pressure along frequency range for mic3

* the plot of error in pressure along frequency range for mic3

##### mic4

* the plot of predicted pressure along frequency range for mic4

* the plot of error in pressure along frequency range for mic4

##### mic5

* the plot of predicted pressure along frequency range for mic5

* the plot of error in pressure along frequency range for mic5

##### plot of error and predicted velocity vs frequency range

##### mic1

* the plot of predicted velocity along frequency range for mic1 (t=10sec)

* the plot of error in velocity along frequency range for mic1 (t=10sec)

* the plot of predicted velocity along frequency range for mic1 (t=30sec)

* the plot of error in velocity along frequency range for mic1 (t=30sec)

* the plot of predicted velocity along frequency range for mic1 (t=50sec)

* the plot of error in velocity along frequency range for mic1 (t=50sec)

##### mic2

* the plot of predicted velocity along frequency range for mic2 (t=10sec)

* the plot of error in velocity along frequency range for mic2 (t=10sec)

* the plot of predicted velocity along frequency range for mic2 (t=30sec)

* the plot of error in velocity along frequency range for mic2 (t=30sec)

* the plot of predicted velocity along frequency range for mic2 (t=50sec)

* the plot of error in velocity along frequency range for mic2 (t=50sec)

##### mic3

* the plot of predicted velocity along frequency range for mic3 (t=10sec)

* the plot of error in velocity along frequency range for mic3 (t=10sec)

* the plot of predicted velocity along frequency range for mic3 (t=30sec)

* the plot of error in velocity along frequency range for mic3 (t=30sec)

* the plot of predicted velocity along frequency range for mic3 (t=50sec)

* the plot of error in velocity along frequency range for mic3 (t=50sec)

##### mic4

* the plot of predicted velocity along frequency range for mic4 (t=10sec)

* the plot of error in velocity along frequency range for mic4 (t=10sec)

* the plot of predicted velocity along frequency range for mic4 (t=30sec)

* the plot of error in velocity along frequency range for mic4 (t=30sec)

* the plot of predicted velocity along frequency range for mic4 (t=50sec)

* the plot of error in velocity along frequency range for mic4 (t=50sec)

##### mic5

* the plot of predicted velocity along frequency range for mic5 (t=10sec)

* the plot of error in velocity along frequency range for mic5 (t=10sec)

* the plot of predicted velocity along frequency range for mic5 (t=30sec)

* the plot of error in velocity along frequency range for mic5 (t=30sec)

* the plot of predicted velocity along frequency range for mic5 (t=50sec)

* the plot of error in velocity along frequency range for mic5 (t=50sec)

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

##### plot of error and predicted pressure vs frequency range

##### mic1

* the plot of predicted pressure along frequency range for mic1

* the plot of error in pressure along frequency range for mic1

##### mic2

* the plot of predicted pressure along frequency range for mic2

* the plot of error in pressure along frequency range for mic2

##### mic3

* the plot of predicted pressure along frequency range for mic3

* the plot of error in pressure along frequency range for mic3

##### mic4

* the plot of predicted pressure along frequency range for mic4

* the plot of error in pressure along frequency range for mic4

##### mic5

* the plot of predicted pressure along frequency range for mic5

* the plot of error in pressure along frequency range for mic5

##### plot of error and predicted velocity vs frequency range

##### mic1

* the plot of predicted velocity along frequency range for mic1 (t=10sec)

* the plot of error in velocity along frequency range for mic1 (t=10sec)

* the plot of predicted velocity along frequency range for mic1 (t=30sec)

* the plot of error in velocity along frequency range for mic1 (t=30sec)

* the plot of predicted velocity along frequency range for mic1 (t=50sec)

* the plot of error in velocity along frequency range for mic1 (t=50sec)

##### mic2

* the plot of predicted velocity along frequency range for mic2 (t=10sec)

* the plot of error in velocity along frequency range for mic2 (t=10sec)

* the plot of predicted velocity along frequency range for mic2 (t=30sec)

* the plot of error in velocity along frequency range for mic2 (t=30sec)

* the plot of predicted velocity along frequency range for mic2 (t=50sec)

* the plot of error in velocity along frequency range for mic2 (t=50sec)

##### mic3

* the plot of predicted velocity along frequency range for mic3 (t=10sec)

* the plot of error in velocity along frequency range for mic3 (t=10sec)

* the plot of predicted velocity along frequency range for mic3 (t=30sec)

* the plot of error in velocity along frequency range for mic3 (t=30sec)

* the plot of predicted velocity along frequency range for mic3 (t=50sec)

* the plot of error in velocity along frequency range for mic3 (t=50sec)

##### mic4

* the plot of predicted velocity along frequency range for mic4 (t=10sec)

* the plot of error in velocity along frequency range for mic4 (t=10sec)

* the plot of predicted velocity along frequency range for mic4 (t=30sec)

* the plot of error in velocity along frequency range for mic4 (t=30sec)

* the plot of predicted velocity along frequency range for mic4 (t=50sec)

* the plot of error in velocity along frequency range for mic4 (t=50sec)

##### mic5

* the plot of predicted velocity along frequency range for mic5 (t=10sec)

* the plot of error in velocity along frequency range for mic5 (t=10sec)

* the plot of predicted velocity along frequency range for mic5 (t=30sec)

* the plot of error in velocity along frequency range for mic5 (t=30sec)

* the plot of predicted velocity along frequency range for mic5 (t=50sec)

* the plot of error in velocity along frequency range for mic5 (t=50sec)

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

##### plot of error and predicted pressure vs frequency range

##### mic1

* the plot of predicted pressure along frequency range for mic1

* the plot of error in pressure along frequency range for mic1

##### mic2

* the plot of predicted pressure along frequency range for mic2

* the plot of error in pressure along frequency range for mic2

##### mic3

* the plot of predicted pressure along frequency range for mic3

* the plot of error in pressure along frequency range for mic3

##### mic4

* the plot of predicted pressure along frequency range for mic4

* the plot of error in pressure along frequency range for mic4

##### mic5

* the plot of predicted pressure along frequency range for mic5

* the plot of error in pressure along frequency range for mic5

##### plot of error and predicted velocity vs frequency range

##### mic1

* the plot of predicted velocity along frequency range for mic1 (t=10sec)

* the plot of error in velocity along frequency range for mic1 (t=10sec)

* the plot of predicted velocity along frequency range for mic1 (t=30sec)

* the plot of error in velocity along frequency range for mic1 (t=30sec)

* the plot of predicted velocity along frequency range for mic1 (t=50sec)

* the plot of error in velocity along frequency range for mic1 (t=50sec)

##### mic2

* the plot of predicted velocity along frequency range for mic2 (t=10sec)

* the plot of error in velocity along frequency range for mic2 (t=10sec)

* the plot of predicted velocity along frequency range for mic2 (t=30sec)

* the plot of error in velocity along frequency range for mic2 (t=30sec)

* the plot of predicted velocity along frequency range for mic2 (t=50sec)

* the plot of error in velocity along frequency range for mic2 (t=50sec)

##### mic3

* the plot of predicted velocity along frequency range for mic3 (t=10sec)

* the plot of error in velocity along frequency range for mic3 (t=10sec)

* the plot of predicted velocity along frequency range for mic3 (t=30sec)

* the plot of error in velocity along frequency range for mic3 (t=30sec)

* the plot of predicted velocity along frequency range for mic3 (t=50sec)

* the plot of error in velocity along frequency range for mic3 (t=50sec)

##### mic4

* the plot of predicted velocity along frequency range for mic4 (t=10sec)

* the plot of error in velocity along frequency range for mic4 (t=10sec)

* the plot of predicted velocity along frequency range for mic4 (t=30sec)

* the plot of error in velocity along frequency range for mic4 (t=30sec)

* the plot of predicted velocity along frequency range for mic4 (t=50sec)

* the plot of error in velocity along frequency range for mic4 (t=50sec)

##### mic5

* the plot of predicted velocity along frequency range for mic5 (t=10sec)

* the plot of error in velocity along frequency range for mic5 (t=10sec)

* the plot of predicted velocity along frequency range for mic5 (t=30sec)

* the plot of error in velocity along frequency range for mic5 (t=30sec)

* the plot of predicted velocity along frequency range for mic5 (t=50sec)

* the plot of error in velocity along frequency range for mic5 (t=50sec)

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

##### plot of error and predicted pressure vs frequency range

##### mic1

* the plot of predicted pressure along frequency range for mic1

* the plot of error in pressure along frequency range for mic1

##### mic2

* the plot of predicted pressure along frequency range for mic2

* the plot of error in pressure along frequency range for mic2

##### mic3

* the plot of predicted pressure along frequency range for mic3

* the plot of error in pressure along frequency range for mic3

##### mic4

* the plot of predicted pressure along frequency range for mic4

* the plot of error in pressure along frequency range for mic4

##### mic5

* the plot of predicted pressure along frequency range for mic5

* the plot of error in pressure along frequency range for mic5

##### plot of error and predicted velocity vs frequency range

##### mic1

* the plot of predicted velocity along frequency range for mic1 (t=10sec)

* the plot of error in velocity along frequency range for mic1 (t=10sec)

* the plot of predicted velocity along frequency range for mic1 (t=30sec)

* the plot of error in velocity along frequency range for mic1 (t=30sec)

* the plot of predicted velocity along frequency range for mic1 (t=50sec)

* the plot of error in velocity along frequency range for mic1 (t=50sec)

##### mic2

* the plot of predicted velocity along frequency range for mic2 (t=10sec)

* the plot of error in velocity along frequency range for mic2 (t=10sec)

* the plot of predicted velocity along frequency range for mic2 (t=30sec)

* the plot of error in velocity along frequency range for mic2 (t=30sec)

* the plot of predicted velocity along frequency range for mic2 (t=50sec)

* the plot of error in velocity along frequency range for mic2 (t=50sec)

##### mic3

* the plot of predicted velocity along frequency range for mic3 (t=10sec)

* the plot of error in velocity along frequency range for mic3 (t=10sec)

* the plot of predicted velocity along frequency range for mic3 (t=30sec)

* the plot of error in velocity along frequency range for mic3 (t=30sec)

* the plot of predicted velocity along frequency range for mic3 (t=50sec)

* the plot of error in velocity along frequency range for mic3 (t=50sec)

##### mic4

* the plot of predicted velocity along frequency range for mic4 (t=10sec)

* the plot of error in velocity along frequency range for mic4 (t=10sec)

* the plot of predicted velocity along frequency range for mic4 (t=30sec)

* the plot of error in velocity along frequency range for mic4 (t=30sec)

* the plot of predicted velocity along frequency range for mic4 (t=50sec)

* the plot of error in velocity along frequency range for mic4 (t=50sec)

##### mic5

* the plot of predicted velocity along frequency range for mic5 (t=10sec)

* the plot of error in velocity along frequency range for mic5 (t=10sec)

* the plot of predicted velocity along frequency range for mic5 (t=30sec)

* the plot of error in velocity along frequency range for mic5 (t=30sec)

* the plot of predicted velocity along frequency range for mic5 (t=50sec)

* the plot of error in velocity along frequency range for mic5 (t=50sec)