# REPORT ON THE RESULTS OBTAINED FROM THE EXPERIMENT (MULTI MICROPHONE METHOD) USING pwelch METHOD (POWER SPECTRAL DENSITY)

## REPORT OF THE ABSOLUTE CALIBRATION

* For the absolute calibration we require acoustic calibrator (MODEL-CAL200) and the microphone is gently inserted into the acoustic calibrator for the calibration
* Output level of the calibrator = $94$ (or) $114 dB$ - tolerance(+- $0.2dB$) at $1KHz$ (+-1% tolerance) frequency
* we have performed two cases for the absolute calibration
- Nominal level 114 dB with signal generated from the calibration (near distance)
- Nominal level 114 dB with signal generated from the calibration (far distance)
- Near distance means the calibrator is kept nearer to the apparatus i.e, DAQ, Signal conditioner, test rig and far distance the calibrator is kept at far distance from the apparatus

### Nominal level 114 dB with signal generated from the calibration (far distance)

* Output level

| Nominal level| rms pressure | Test result | Lower limit | upper limit | lying in the range | result |
| -------- | -------- | -------- | --- | --- | --- | --- |
| 114 dB | 9.0182 Pa | 113.818dB | 113.80dB |114.20dB | yes | pass |

* Frequency

| Nominal level| rms pressure | Test result | Lower limit | upper limit | lying in the range | result |
| -------- | -------- | -------- | --- | --- | --- | --- |
| 114 dB | 9.0182 Pa | 1000.58Hz | 990 Hz |1010 Hz | yes | pass |

* plot of pressure-time domain
- For the time interval 50sec to 90sec the p-t graph is constant, it is shown below

* The graph of pressure frequency domain after doing fft

* phase plot for the time interval is shown as below (radians)

### Nominal level 114 dB with signal generated from the calibration (near distance)

* Output

| Nominal level| rms pressure | Test result | Lower limit | upper limit | lying in the range | result |
| -------- | -------- | -------- | --- | --- | --- | --- |
| 114 dB | 10.6195Pa | 114.05014dB | 113.80dB |114.20dB | yes | pass |

* Frequency

| Nominal level| rms pressure | Test result | Lower limit | upper limit | lying in the range | result |
| -------- | -------- | -------- | --- | --- | --- | --- |
| 114 dB | 10.6195Pa| 1000.59Hz | 990Hz |1010Hz | yes | pass |

* plot of pressure-time domain
- For the time interval 10sec to 40sec the p-t graph is constant, it is shown below

* The graph of pressure frequency domain after doing fft

* phase plot for the time interval is shown as below (radians)

## RELATIVE CALIBRATION OF MICROPHONES

### RESULTS OBTAINED

* We have done three cases for the relative calibration i.e, three types of signals were given to the speaker
- sine wave with amplitude 2mV, frequency 200Hz and time 100sec
- chirp signal with amplitude 1mV, frequency from 250Hz-2500Hz and time 100sec
- chirp signal with amplitude 2mV, frequency from 250Hz-2500Hz and time 100sec

### sine wave with amplitude 2mV, frequency 200Hz and time of 100sec

* the pressure time series data of the 5 microphones which includes absolutely calibrated microphone is shown below


* the pressure time series data of the five microphones with time shown upto 1sec in the box.


* the pressure time series data of the five microphones with time shown upto 5sec in the box.


* the pressure frequency domain of the five microphones is shown below


* the detailed view of pressure frequency domain for the five microphones is shown below


* rms value of pressures of the microphones are shown below

| rms value of the pressure | value |
| ----------- | ----------- |
| rms voltage of input signal | $\sqrt2$ mV
| absolutely calibrated | $5.0945$ Pa |
| microphone 1 | $4.3759$ Pa|
| microphone 2 | $3.8967$ Pa |
| microphone 3 | $6.2414$ Pa |
| microphone 4 | $4.2038$ Pa |

### chirp signal with amplitude 1mV, frequency from 250Hz-2500Hz and time 100sec

* the pressure time series data of the 5 microphones which includes absolutely calibrated microphone is shown below


* the pressure time series data of the five microphones with time shown upto 1sec in the box


* the pressure time series data of the five microphones with time shown upto 5sec in the box


* the pressure frequency domain of the five microphones is shown below


* the detailed view of pressure frequency domain for the five microphones is shown below


* rms value of pressures of the microphones are shown below

| rms value of the pressure | value |
| ----------- | ----------- |
| rms voltage of input signal | $0.7053$ mV
| absolutely calibrated | $2.4462$ Pa |
| microphone 1 | $2.7339$ Pa|
| microphone 2 | $2.7433$ Pa |
| microphone 3 | $3.0999$ Pa |
| microphone 4 | $3.2027$ Pa |

### chirp signal with amplitude 2mV, frequency from 250Hz-2500Hz and time 100sec

* the pressure time series data of the 5 microphones which includes absolutely calibrated microphone is shown below


* the pressure time series data of the five microphones with time shown upto 1sec in the box


* the pressure time series data of the five microphones with time shown upto 5sec in the box


* the pressure frequency domain of the five microphones is shown below


* the detailed view of pressure frequency domain for the five microphones is shown below


* rms value of pressures of the microphones are shown below

| rms value of the pressure | value |
| ----------- | ----------- |
| rms voltage of input signal | $\sqrt2$ mV
| absolutely calibrated | $3.1395$ Pa |
| microphone 1 | $3.5455$ Pa|
| microphone 2 | $3.5019$ Pa |
| microphone 3 | $3.6339$ Pa |
| microphone 4 | $3.9622$ Pa |

### Calibration coefficients of microphones with respect to absolutely calibrated microphone

#### Sine wave with amplitude 1mV, frequency from 250Hz-2500Hz and time 100sec

* magnitude of pressure with respect to absolutely calibrated microphone ($\frac{p_{ref}}{p_j}$)

* magnitude of phase with respect to absolutely calibrated microphone ($\phi_{ref}$-$\phi_{j}$)

#### Chirp signal with amplitude 1mV, frequency from 250Hz-2500Hz and time 100sec

* magnitude of pressure with respect to absolutely calibrated microphone ($\frac{p_{ref}}{p_j}$)


* magnitude of phase with respect to absolutely calibrated microphone ($\phi_{ref}$-$\phi_{j}$)


#### Chirp signal with amplitude 2mV, frequency from 250Hz-2500Hz and time 100sec

* magnitude of pressure with respect to absolutely calibrated microphone ($\frac{p_{ref}}{p_j}$)


* magnitude of phase with respect to absolutely calibrated microphone ($\phi_{ref}$-$\phi_{j}$)


## 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 $1mm$

### WITH FOAM AT SPEAKER END

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

* the pressure time series data of the 5 microphones is shown below

* the frequency domain of the five microphones is shown below

* the power spectral density of the five microphones is shown below

* the plot of the reflection coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (calculated using pwelch method)

* the plot of the absorption coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (calculated using pwelch method)

* the plot of the real and imaginary part of impedance vs frequency range at the open end i.e, at $x=0$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

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

* the pressure time series data of the 5 microphones is shown below

* the frequency domain of the five microphones is shown below

* the power spectral density of the five microphones is shown below

* the plot of the reflection coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (calculated using pwelch method)

* the plot of the absorption coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (calculated using pwelch method)

* the plot of the real and imaginary part of impedance vs frequency range at the open end i.e, at $x=0$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

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

* the pressure time series data of the 5 microphones is shown below

* the frequency domain of the five microphones is shown below

* the power spectral density of the five microphones is shown below

* the plot of the reflection coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (calculated using pwelch method)

* the plot of the absorption coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (calculated using pwelch method)

* the plot of the real and imaginary part of impedance vs frequency range at the open end i.e, at $x=0$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

### WITH OUT FOAM AT SPEAKER END

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

* the pressure time series data of the 5 microphones is shown below

* the frequency domain of the five microphones is shown below

* the power spectral density of the five microphones is shown below

* the plot of the reflection coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (using pwelch method)

* the plot of the absorption coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (using pwelch method)

* the plot of the real and imaginary part of impedance vs frequency range at the open end i.e, at $x=0$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

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

* the pressure time series data of the 5 microphones is shown below

* the frequency domain of the five microphones is shown below

* the power spectral density of the five microphones is shown below

* the plot of the reflection coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (using pwelch method)

* the plot of the absorption coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (using pwelch method)

* the plot of the real and imaginary part of impedance vs frequency range at the open end i.e, at $x=0$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

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

* the pressure time series data of the 5 microphones is shown below

* the frequency domain of the five microphones is shown below

* the power spectral density of the five microphones is shown below

* the plot of the reflection coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (using pwelch method)

* the plot of the absorption coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (using pwelch method)

* the plot of the real and imaginary part of impedance vs frequency range at the open end i.e, at $x=0$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

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

* the pressure time series data of the 5 microphones is shown below

* the frequency domain of the five microphones is shown below

* the power spectral density of the five microphones is shown below

* the plot of the reflection coefficient vs frequency range i.e, 250Hz-2500Hz is shown below (using pwelch method)

* the plot of the absorption coefficient vs frequency range i.e, 250Hz-2500Hz is shown below

* the plot of the real and imaginary part of impedance vs frequency range at the open end i.e, at $x=0$

* the plot of pressure along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$

* the plot of velocity along the length of tube for time interval of $t=0-50sec$ with a step of $t=10sec$