www.miqel.com/.../vibrational-truth.html <http://www.miqel.com/jazz_music_heart/vibrational-truth.html>

Sound Waves

Resonance, Frequency and the Musical Scale

Natural Frequency

- All objects have a natural frequency at which they vibrate or resonate when struck, plucked strummed etc.

-Each natural frequency is a standing wave.

-An object's natural frequency is the frequency that allows it to vibrates with the least input of energy.

http://www.youtube.com/watch?v=O9FrMkhQoA4&safe=active

Mythbusters Shattered Glass

Natural Frequency versus Resonance

Natural Frequency - the frequency an object will tend to vibrate at when struck or disturbed.

Forced Vibration - the tendency of one vibrating object to force another CONNECTED object to vibrate. This causes an increase in amplitude.

Resonance - when one vibrating object causes another to vibrate without directly touching the second object.

https://www.youtube.com/watch?v=wvJAgrUBF4w

Beat Frequency

When two (or more) sound waves of nearly equal frequency are played at the same time, the constructive and destructive interference has a predictable pattern of large and small amplitudes.

The Beat Frequency is

Δf =Ιf2 - f1 Ι

Humans can hear a beat frequency of less than 7 Hz.

https://www.youtube.com/watch?v=aCocQa2Bcuc

Note: The sound waves are shown as transverse (or sine waves) for ease of drawing. Sound waves are longitudinal waves.

Pitch verses Frequency

-Frequency is the number of cycles/second.

-Pitch is the perceived frequency of a sound.

ie. a musician hears 256 Hz and 512 Hz as the same pitch or note. (in this case a C ).

http://www.virtualpiano.net/

Musical Scale

European tradition divides the musical Octave into 12 notes.The 12th note is the same note as the first only an octave higher.

Other musical systems divide the scale into between 42 and 360 notes. In each system the last note of the scale has twice the frequency of the first note.

The Ratio of Frequencies for octaves is:

2:1Second Octave Frequency : First Octave Frequency

up 1 octavedown 1 octave

Example

Middle C = 256 Hz

C note 1 octave below =

A note is a single tone, pitch or frequency.A doubling of the frequency of any note produces a higher note with the same pitch, as in middle C and high C on a piano. This is known as an Octave.

Octaves go on forever above and below our musical scale, they are simply halving's or doublings of frequency.

A chord is any two notes or pitches played simultaneously.

All chords produce certain sounds which are unique because whenever two notes are played together, a third note or beat is also heard.

Musical Scale

The most basic scale is called the diatonic scale.

C D E F G A B C1 D1

4 -- 5 -- 6 4 -- 5 -- 6

4 -- 5 -- 6

Major Triad - a collection of three notes with frequencies in the ratio

4: 5: 6

There are three triads in each octave.

Example 1

Middle C = 256 Hz

E note =

G note =

4: 5: 6 major triadC:E:G

E 5C 4

=

E 5C 4where C = 256 Hz

=

Example 2

C1 note = 512 Hz

A note =

F note =

http://www.ted.com/talks/yoav_medan_ultrasound_surgery_healing_without_cuts

Homework:

White booklet

Read pages 17-23Complete questions 8-11 page 25

Pink Booklet

questions 1-5 pages 7 and 8