# 'Discover the underlying mathematics behind music'

Do you like music?  If you play a musical instrument you’ll know that some combinations of notes sound great, and others sound dreadful.  In this investigation you are going to discover that it is mathematics that lies behind these notes, chords and harmonies.  Tuning forks are used to tune instruments.  Mathematically they are interesting since they produce pure tone sound – there is no echo like with a piano or guitar body, for example. You are going to listen to some different tuning fork sounds and look at the visual representation of these sounds.  By reproducing the graphs of these sounds for yourself you should understand how they are related to the musical scale.

### Resources & Description

• For this activity you will need some graphing software
• Use graphing software to explore the effect of changing a and b in the equation y = asinbx
• Here is the main part of the activity  The Mathematics of Sound to be attempted after watching video instructions
• Check your understanding: try this QUIZ to see if you can apply what you have learned.

Amplitude & Frequency
1. Learn how the value of a affects the amplitude of the sine curve y = asinx

Which of the following graphs have an amplitude of 2 [Show][Hide]

1. y=sin2x
2. y=0.5sinx
3. y=2sinx
4. y=sin(0.5x)
Explanation:

2. What is the amplitude of the graph y = -3sin 2x ? [Show][Hide]

1. 2
2. 1/3
3. -3
4. 3
5. 1/2
Explanation:

3. Learn how the value of b affects the period of the sine curve y = sinbx

Which of the following graphs has a period of 360°? [Show][Hide]

1. y=360sinx
2. y=sin360x
3. y=sinx
4. y=sin(x/360)
Explanation:

4. What is the period of the graph of y=sin2x? [Show][Hide]

1. 2
2. 360°
3. 720°
4. 180°
Explanation:

5. Which of the following graphs has a period of 30°? [Show][Hide]

1. y=sin30x
2. y=sin12x
3. y=sin(x/12)
4. y=sin(x/30)
Explanation:

6. Which of the following graphs has a period of 1°? [Show][Hide]

1. y=sinx
2. y=sin(x/360)
3. y=360sinx
4. y=sin360x
Explanation:

7. Which of the following graphs has a period of 0.1°? [Show][Hide]

1. y=sin3600x
2. y=0.1sinx
3. y=sin0.1x
4. y=sin10x

• The following applet should help you understand the dynamics of sound  Sound Wave
• The following short video shows a recording of a pitching fork (pitch A) from http://www.onlinetuningfork.com/and then a visual representation of the sound recorded with Audacity, a sound recording piece of software.

• The following video gives an introduction to the activity.  Watch it to see the shape of the graph of pitch A4

### Video Instructions

A visual representation of the A4 pitch