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# Search>Learning Exercise Results> Complex Waves

## Learning Exercise: Complex Waves

Title:
Complex Waves
Material:
Description:
This is an undergraduate lab assignment using the software Overtone. It illustrates the concept of repeat time, the missing fundamental, harmonics, and phase changes for the initial experimental module in Overtone. The second experimental module is a spectrum analyzer and the lab question for this analyzes the two-tone combinations present in a land-line telephone keypad, which create a pattern.
Course: Acoustics

Submitted by:
Susan Phillips
January 26, 2011

### Exercise

Complex Waves Name______________________ I. A. Find the Synthesizer Control Panel in the Overtone software. At the first panel, change the fundamental frequency to 910 Hz and raise the amplitude to 50 dB. Copy and paste the resulting waveform. What is the period of the wave? Add in the 5th harmonic. Draw the summed (bottom panel) waveform again. What is the repeat time? Change the phase of the fundamental to 180 degrees. Copy and paste the combined waveform. Return the phase to 0 degrees. Add in the 7th harmonic. Copy and paste the summed waveform again. What is the repeat time? Copy and paste the Frequency spectrum. Add in the 9th harmonic. Draw the summed waveform again. What is the repeat time? Increase the amplitude of the 1st harmonic to 100 dB. Copy and paste the summed waveform. Turn off the fundamental. Copy and paste the summed waveform. What is the repeat time? B. Change the fundamental frequency to 220 Hz. Turn the fundamental tone on, then the 2nd harmonic. Copy the waveform. Then change the phase of the 2nd harmonic to 180o and copy the waveform again. Does the complex look any different when you change the phase? Does it sound any different when you change the phase? Why? 2. Under File, Choose Experiments, then Analyzer in Overtone. In the Analyzer Control Panel, turn off the Trigger by un-checking the box. Change the frequency range from 20,000 Hz to 2000 Hz. Hook up a microphone to your computer. Hold your telephone earpiece up to the microphone, press the #1 on the phone, and click Run on the control panel. You should get a nice clear 2-pt frequency analysis in the lower box labeled Frequency Window. Click on stop before you take the phone away from the microphone. Print the screen to Paint and select the Frequency Window to paste into the lab here. Do this for every number on your phone. Then indicate the frequencies used for each number on the diagram below. Is there a pattern?

### Audience

• College Lower Division
• College Upper Division

### Topics

complex acoustic waveforms, spectrum analysis

### Requirements

Understanding of sine waves

### Learning Objectives

Students will: determine repeat time of a complex waveform. read a Fourier analysis of a complex waveform do a real-time spectral analysis of a complex waveform.

• Core Activity
• Individual
• Student-centered
• Unsupervised

### Assessment

Complex Waves Key _______ I. Find the Synthesizer Control Panel in the Overtone software. At the first panel, change the fundamental frequency to 910 Hz and raise the amplitude to 50 dB. Copy and paste the resulting waveform. What is the period of the wave in milliseconds (ms)? 910 Hz at 50 dB The period is 1.1 ms. Add in the 5th harmonic. Draw the summed (bottom panel) waveform again. What is the repeat time? Change the phase of the fundamental to 180 degrees. Copy and paste the combined waveform. Return the phase to 0 degrees. 910 Hz at 50 dB with 5th harmonic Again 180 degrees out of phase Repeat time is 1.1 ms. Add in the 7th harmonic. Copy and paste the summed waveform again. What is the repeat time? Copy and paste the Frequency spectrum. 910 Hz w/5th & 7th harmonics Frequency spectrum for this complex wave The repeat time is still 1.1 ms. Add in the 9th harmonic. Draw the summed waveform again. What is the repeat time? Increase the amplitude of the 1st harmonic to 100 dB. Copy and paste the summed waveform. 910 Hz w/5th, 7th, 9th harmonics Again at 100 dB 1st harmonic The repeat time is still 1.1 ms. Turn off the fundamental in the first box. Copy and paste the summed waveform. What is the repeat time? 910 Hz removed from complex waveform Even without the fundamental, the repeat time is still 1.1. ms. B. Change the fundamental frequency to 220 Hz. Turn the fundamental tone on, then the 2nd harmonic. Copy the waveform. Then change the phase of the 2nd harmonic to 180o and copy the waveform again. Does the complex look any different when you change the phase? Does it sound any different when you change the phase? Why? 220 Hz w/ 2nd harmonic 2nd harmonic 180 degrees out of phase It looks different but doesnâ€™t sound different. Humans cannot hear phase changes. 2. Under File, Choose Experiments, then Analyzer in Overtone. In the Analyzer Control Panel, turn off the Trigger by un-checking the box. Also in the right panel, change the frequency range to 2000 Hz instead of 20,000. Hook up a microphone to your computer. Hold your telephone earpiece up to the microphone, press the #1 on the phone, and click Run on the control panel. You should get a nice clear 2-pt frequency analysis in the lower box labeled Frequency Window. Click on stop before you take the phone away from the microphone. Print the screen to Paint and select the Frequency Window to paste into the lab here. Do this for every number on your phone. Then indicate the frequencies used for each number on the diagram below. If you put your cursor on the peak, the frequency will show up in the upper left corner of the box. Is there a pattern? Number 1: 700 and 1200 Hz 1200 Hz 1336 Hz 1480 Hz
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