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## ACOUSTICS LAB

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**ACOUSTICS LAB**ME4053 Objectives: Study the propagation of sound waves from a loudspeaker and compare with a simple theoretical model Specifically: • Measure the speed of sound • Show that acoustic pressure falls off like 1/R in the far-field • Study the speaker directivity, harmonic distortion, and frequency response Do not use this in your report. Write the objectives etc in your own words To see presentation details: View>>Notes Page in PowerPoint**Experimental Procedure for:**• Speed of sound measurement • 1/R acoustic pressure behavior in far-field Note: signal parameter values vary from A-sections to B-sections and from semester to semester. Refer to “Procedures” document for numerical values • Keep the speaker fixed • Vary the mic distance, R • Record time delay • Record rms voltage**Experimental Procedure for**Capturing Sample a Waveform Save waveforms to Floppy Drive: • Move mic a distanceR_w from baffle • Save input waveform • Save output waveform • See later slide for processing**Experimental Procedure for Harmonic Distortion and Frequency**Response • Obtain Harmonic Distorion: • Fix mic at distance R_df • Use Oscilloscope Math FFT • Record amplitude at a “loud” volume • Decrease volume until main peak is 12dB lower • Record magnitude of second peak • Obtain Frequency Response: • Record the RMS voltage of the microphone over a set of frequencies at two different speaker angles.**Experimental Procedure (cont’d)**• Get your notebook signed • Turn all equipment off (especially the mic!) • Leave the lab (you don’t have to go home but you can’t stay here)**T**T Time Delay & RMS Voltage Measurements @ = xx s ∆ = xx s Ch 2 = xx V RMS Ch 1 Input Gating ON gives RMS value only between two cursors Ch 2 Output @ ∆ ∆ should remain constant as it is simply the period of the burst @ gives distance from trigger to solid cursor. This is an easy way to measure time delay.**Post-Lab Data Analysis for Sound Pressure Level**• Calculate sound pressure level (SPL) in terms of decibels (dB) • Plot the SPL as a function of log(R/Rmin) • Verify that the SPL approaches a -20 dB/decade slope sufficiently far from the speaker**Sound Pressure Level (SPL) Decay**SPL decay approaches 1/R (-20dB per decade) model in far field (students may look different)**Post-Lab Data Analysis forSpeed of Sound**Plot the data: • Perform a regression on the data • Be sure you have at least 4 significant digits in the slope estimate • Calculate theoretical value of speed of sound • Estimate the “standard error” in your result using the formulas on the next slide • You may want to use Matlab’s “regress” function or Excel’s “linest” function to calculate s est • Compare theoretical and experimental values**Error Analysis**Standard Error of the tarr Estimate Standard Error of the Slowness (Slope) Estimate Data Arrival Time (m sec) Range(m)**Post-Lab Data Analysis for Captured Waveform**• Compare input and output signal • Plot .input and output signals using Matlab. The “subplot” command is useful for this • Discuss the differences between waveforms • Note: t=0 on the abscissa is the trigger point for input signal • (The results shown below are for a 5 kHz 10 cycle signal )**Post-Lab Analysis for Frequency Response and Harmonic**Distortion • Plot the Frequency Response for both the directly facing and 70 degree speaker data. • Convert the voltages to dB using: 20*log10(voltage) • Use directivity theory: Theoretical 70 degree response is equal to 20*log10(voltages@0 degrees) – absolute(20*log10(D(theta))) see future slide for D(theta) and plot. • Then plot in Matlab: semilogx(frequencies, dBvalues) • Take an average dB over 150-12800 Hz and calculate the distance to the largest outlier in that rage. • Harmonic Distortion calculate the dB ratios, is the speaker more pure at lower volumes?**Frequency Response Example Plot**Based on this plot can you tell if higher or lower frequencies are more directive and does this speaker provide a flat response over this frequency range?**Post-Lab Data Analysis Directivity Help**• Theoretical directivity pattern • Where: k is the wave number, a is the radius of the source, and J1 is a bessel function of the first order. • At low frequencies (where l > a), the function D(q) does not exhibit many variations as a function of q ==> speaker is weakly directional • At higher frequencies (when l < a), D is more dependent on the values of q ==> the speaker is highly directional**Sample code to read comma delimited text file in Matlab**%This file will read a comma delimited file %generated from the Tektronix Oscilloscope %It will then plot the data % %Created by: Wayne M. Johnson 17MAR03 % clear all; %clears all variables close all; %closes all figure windows a=dlmread('TEK00000.CSV'); %reading comma delimited file tin=a(:,1)*1e3; %assigning the time data %Note that time data has been shifted to such that %t=0 corresponds to the trigger point for input signal. % See Tektronix User Manual, p. 3-47 Vin=a(:,2); %assigning the voltage data a=dlmread('TEK00001.CSV'); %reading comma delimited file tout=a(:,1)*1e3; %assigning the time data Vout=a(:,2); %assigning the voltage data %plotting data subplot(2,1,1); plot(tin,Vin);grid %plotting the data title('Input signal XXX kHz');ylabel('Voltage (V)'); subplot(2,1,2); plot(tout,Vout);grid %plotting the data title('Microphone output at YYY cm from speaker'); xlabel('Time (msec)');ylabel('Voltage (V)');**Last minute pointers**• Your presentations should be much better than this one. Use your own words! • For help contact the TA’s • See Class syllabus for Dates/Times of Presentations and Abstract Submission • Both submissions will be done with your group