Harmonics
Introduction

You can probably recognize the difference between a note played on a piano and the same note played on a trumpet. This is because the two sounds have different tone or quality. The instruments do not make pure notes, but they are combinations of pure notes.
Making music
The main
frequency
In general, the frequency of an event describes how often it occurs. When talking about waves, the frequency is a measure of how many waves go past a fixed point in a given time.
frequency
of a sound is often called the first harmonic. This is the frequency that determines the pitch of the note.

Push the button labelled '1st' in the circuit in Fig.1 below to listen to the first
harmonic
In music, harmonics of a note are integer multiples of the original note. They add depth to the note.
harmonic
. The frequency of this note is 250 Hz. Look at the waveform on the graph at the bottom of the page. It should be a simple wave that moves smoothly up and then down. This is the form of a pure note.

The second harmonic has a frequency of 500 Hz. This is double that of the first harmonic. The first and second harmonics sound good when played together. In musical terms these two are the same notes, separated by one octave. Push the button labelled '2nd' to listen to these two together. Look at the trace on the graph.

Click on the figure below to interact with the model.

 Figure 1.  A circuit for investigating harmonics.

When you play the 1st and 2nd harmonics together, is the waveform on the CRO still a pure wave?

Alternate between playing the first harmonic and the first and second together. Compare the wavelengths of the two waveforms.

When you play the 1st and 2nd harmonics together, does the frequency of the overall wave change?

The third harmonic has a frequency which is triple that of the first harmonic.

What is the frequency of the third harmonic?

Set the value of the third signal
generator
A generator is a device that creates electrical energy.
generator
to this value. To do this, click on the frequency above the green signal generator and edit the number. Now push the button labelled "3rd" to play the first, second, and third harmonics together.

Fill in this table for the remaining three harmonics:

•  Harmonic Frequency (Hz) 1st 250 2nd 500 3rd 750 4th 5th 6th

Now set the last three signal generators to their corresponding frequencies. Try pressing the different buttons to play the first harmonic with a different number of additional harmonics. Can you tell the difference in the sound? You should find that the harmonics add depth and richness to the pure note.

Telephone dialling tones
Press the dial tone button in Fig.2 below. This should be the sound you hear from a telephone – the dialling tone. It is made of two frequencies: 350 Hz and 440 Hz. These are not harmonics, but they sound good together.

Click on the figure below to interact with the model.

 Figure 2.  Part of the circuit inside a telephone.

Try pressing the different numbered buttons on the telephone dial pad in Fig.2. The tone for each number is made up of two individual frequencies. For example, number 1 is made up of a note at 697 Hz and one at 1209 Hz.

Which of the following buttons also uses a note at 1209 Hz?

The actual value of the frequencies is not as important as the difference between them. When you press a button on your phone, the electrical signal travels down the phone line to the telephone exchange. At the exchange, the difference between the frequencies is calculated. From this, the button you pressed can be determined.

What is the difference between the two frequencies that are played when you press 8?

Phones that dial like this are called 'tone dialling'.

Until recently all phones used pulse dialling. In this system, each dialled digit generates the same number of pulses as the number itself. For example when you dial a 4, the phone produces 4 pulses or clicks, which you can hear in the handset. Because only one pulse of sound is needed in tone dialling, it is much quicker than pulse dialling. It can be used for automated replies (e.g. 'Press 2 if you want more information').

Summary

Musical notes are rarely pure waves, but are mixtures of several harmonics.

Harmonics add tone or quality to the note. Tone is what makes a piano sound different to a trumpet.

Telephones use two frequencies combined to perform tone dialling.
Exercises
1. The table below shows the first 6 harmonics of a note. Fill in the gaps to complete the table.

•  Harmonic Frequency (Hz) 1st 2nd 3rd 450 4th 5th 6th

2. Several harmonics of a note are displayed on a CRO. Match each graph below with the correct number of harmonic.
 Figure 3.
3. Two sounds are recorded and displayed on a CRO as shown in Fig.3 above. Decide whether the following properties are the same or different.
•  Frequency: Different Same Amplitude: Different Same Quality: Different Same Wavelength: Different Same Tone: Different Same Volume: Different Same

Click on the figure below to interact with the model.

 Figure 4.

4. Part of the circuit inside a telephone is shown in Fig.4 above. Complete the table below to show the frequencies for each button.

•  Button High Frequency Low Frequency Frequency Difference 0 1 1209 697 512 2 3 4 5 6 7 8 9 * #

5. What is the name for the type of dialling this phone uses?
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