1. Chapter 12
Parts of waves (review)
Octaves
Stringed Harmonics
How to produce sound
Open/Open Harmonics
Open/Closed Harmonics
Harmonics/Fundamentals

2. Single wave pulse travels
Transverse waves
Single wave pulse travels
Transverse waves:
Transverse waves:
The particles of the disturbed medium move perpendicular to the wave motion
particle
wave

3. Longitudinal waves Longitudinal waves: Longitudinal waves:
compression travels
Longitudinal waves:
The particles of the disturbed medium move parallel to the wave motion
Longitudinal waves:

4. Basic Variables of Wave Motion
Terminology to describe waves
Crest: “Highest point” of a wave
Wavelength l: Distance from one crest to the next crest.
Wavelength l: Distance between two identical points on a wave.
Period T: Time between the arrival of two adjacent waves.
Frequency f: 1/T, number of crest that pass a given point per unit time

5. Sound
- is a wave (sound wave)
- Rarefied and compressed regions
Longitudinal wave
air molecules move back and forth

6. Sound Waves Sound waves are longitudinal waves.
They consist of compressed and rarified regions of gas (medium)
We can hear (audible) frequencies from about 20 Hz (low) to 20,000 Hz (high).
Infrasonic “sound” waves: below ~ 20 Hz
Ultrasonic sound waves: above ~ 20,000 Hz
The speed of sound in air: c ~ 343 m/s ~ 740 mi/hr ~ 0.2 mi/sec. (dry air, 68F)

7. Question #1 It is a dark and stormy night.
Lightning strikes in distance.
You see the lighting, then, after ten seconds you hear the thunder.
How far away did the lighting strike?
1 mile
2 miles
3 miles
4 miles
5 miles

8. Notes and their fundamental frequency
Octaves: frequency doubles for each tone
**Note** An octave will double in frequency each time and this is different than Harmonics

9. For example: Find middle C (C4) on the chart to the right.
Middle C has a frequency of Hz, one octave higher is C5 which has a frequency of Hz, two octaves higher (C6) has a frequency of Hz.
Middle C can also be the fundamental frequency ( Hz) and this is the 1st Harmonic, the 2nd Harmonic (f = Hz) is the same as one octave higher, but the 3rd Harmonic (f = Hz) is NOT the same as two octaves higher.

10. Creating standing waves:
When two waves are traveling back and forth, under the right conditions (right frequency), we can create standing waves.
Standing waves have stationary nodes and antinodes
Examples we’ll talk about this chapter:
Standing waves on a string.
Standing waves in a pipe (open and closed).

11. String Harmonics frequency L 2f1 3f1 4f1 5f1 6f1
L … Length of string; n … harmonic v … velocity of sound

12. Standing waves have stationary nodes and anti-nodes
L … Length of string
n … harmonic

13. Fundamental Frequency
String vibrates as a single arc, up and down
velocity antinode occurs at center of string
This is the fundamental frequency mode
Pitch (frequency of vibration) is
inversely proportional to string length

14. Harmonics (Overtones)
In addition, string can vibrate as
two half-strings
three third-strings
etc.
These are higher-order frequency modes
These modes have higher pitches – overtones

15. Harmonics in a String In a string, the harmonic pitches are
two times the fundamental frequency (octave)
three times the fundamental frequency
etc.
These integer multiples are called overtones
A string harmonics will have all harmonics.
i.e. 2nd, 3rd, 4th, 5th, etc.

16. Producing Sound Thin objects don’t project sound well
Air flows around objects
Compression and rarefaction is minimal
Surfaces project sound much better
Air can’t flow around surfaces easily
Compression and rarefaction is substantial
Many instruments use surfaces for sound

17. Open pipe:

18. Fund. Frequency
v… speed of sound
v = 343 m/s in air at 20 °C

19. Open/open tube

20. A wave reflecting off of the boundary
At an open boundary: the air bounces moving in and out of the boundary.
Demo boundary conditions with string and cable
motions

21. Harmonic Vibrations for open-open
In addition, column of air can vibrate as
two half-columns
three third-columns
These higher-order modes are the harmonics
Pitches are integer multiples of the fundamental
Open/open tube has all integer multiples f,2f,3f,4f,5f OR 1st, 2nd, 3rd, 4th, 5th, etc. (just like a stringed instrument)
A open-open tube will have an anti-node at each open end

22. Fundamental frequency:
open-closed pipe:

23. Open/closed tube

24. Wave reflecting off of the closed boundary
At a closed boundary: the wave reflects if it has a high pressure at the wall. The air compresses at the wall and then bounces back.

25. Harmonic Vibrations for closed-open
These higher-order modes are the harmonics
Pitches are odd multiples of the fundamental
Closed/open tube only has odd harmonics (e.g., clarinet) f, 3f, 5f, 7f OR 1st , 3rd, 5th, 7th, etc.
A closed-open tube will have a node at the closed end

26. Question #2
You play an open organ pipe with a length of 1m.
What is the fundamental frequency?
1 Hz
86 Hz
172 Hz
343 Hz
686 Hz
Now you close the pipe at one end. What will the frequency be then?

27. Standing waves or modes in a column of air
Question #3
Standing waves or modes in a column of air
The motions shown are air speeds
One of these is a pipe that is closed on one end and the other is open on both ends. Which one is which?

28. Which one has a lower fundamental frequency? Open/open or open/closed?
Question #4
Which one has a lower fundamental frequency? Open/open or open/closed?
closing end of flute!
Open/open open/closed

29. Fundamental Frequency review
Air column vibrates as a single object
Pressure antinode occurs at center of open column
Velocity antinode occurs at ends of open column
Pitch (frequency of vibration) is
inversely proportional to column length
inversely proportional to air density
A closed pipe vibrates as half an open column
pressure antinode occurs at sealed end
Velocity node occurs at the sealed end
frequency is half that of an open pipe