Making a Picture of Your Voice using Sine Waves
Violin Waveform

Purpose

Each person's voice has a distinctive sound which is built up from acoustic waves. We will find the amplitudes and frequencies making up your voice and plot your voice waveform using a combination of sine waves.

Materials needed:

Laptop (MS Windows) with microphone (most laptops have them built in)
Make sure your volume control is not muted.

Download this "Spectrum Analyser"

Here:
SpecAn_2v8.exe

or any of these:
http://www.techmind.org/
Soundcard Audio Tools and Toys
Real-time Spectrum Analyser

or:
do a search: spectrum analyser william steer

After downloading, double click this program to run it (Windows only).

Axes description for Spectrum Analyser:
A frequency scale on the horizontal axis in kHz (1000 cycles per second - a cycle is one period)
An amplitude scale on the vertical axis (in decibels, but don't worry about that - just call each tick mark 1 unit) .
You can adjust the amplitude for the sensitivity of your microphone under "Vertical Scale" at the upper left.

Part I - Preliminary Trig

For the following, we will assume the horizontal axis units are time (sec)

1. If f(t) = 2sin(8πt), what is the period of f(t)? sec; Frequency? (Hz or cycles/sec); Amplitude? units

2. If the frequency of a sin function is 100 Hz and amplitude = 5, what is the period? sec; f(t) =

Part II - Finding the function for your voice

3. Press START; Have the best whistler in your group whistle into the mic. Hit STOP to hold it.
Normally you see a single peak.

a. What does changing the loudness of your whistle due to the peak?

b. What does changing the pitch of your whistle due to the peak?

c. Estimate the frequency and amplitude of a typical whistle. Use these to write the sin function for the whistle.

w(t) =

4. Press START; Have someone say and hold "O" into the mic. Hit STOP to hold it.

You will see several peaks (only use the major ones - 4 or fewer peaks). Estimate the frequency and amplitude of each peak and find the sin function for each. Your voice is the sum of of these functions! The analyser has separated them out for you.

Write your voice function for "O" here: v(t) =

Plot this function v(t) on your grapher. The t axis represents time and the y axis represents amplitude.

Note on scaling the horizontal axis:
Since the frequencies in w(t) are so high, your t scale numbers will have to be spread out (very small).
For example, at a frequency of 1000 Hz, there are 1000 waves in 1 sec. To get started, figure out the period of your lowest frequency and use this is a unit on the horizontal axis.
Keep adjusting the window scale until you get the smoothest waveform.

Show your scale on each axis!