1. Review – Standing Waves
What are the things that can affect the velocity of a string?
The force of tension and thickness of string (linear density)
What are the two parts of a standing wave? Which part produces the most sound?
Nodes – little to no movement
Anti-node – lots of movement
Anti-node produce the most sound
Term for the ‘voice’ of the instrument?
Timbre

2. Difference Between Notes and Noise
Sound (musical notes) will have some sort of repeating pattern

3. Standing Waves w/ Musical Instruments
Tuning Forks – Produce one frequency (pure tone)
Musical instruments sound different from tuning forks – due to their timbre (tone quality or tone color)
Difference in timbre – due to the instruments harmonics
When a note is played, the primary sound = Fundamental frequency
Within each fundamental frequency are other frequencies – The harmonics

4. Standing Waves - Strings
Different frequencies are produced by different harmonics
Fundamental
First Harmonic (f1)
Number of Loops = 1
Second Harmonic (f2)
Number of Loops = 2
f2 =2(f1)
Third Harmonic (f3)
Number of Loops = 3
f3 =3(f1)
Fourth Harmonic (f4)
Number of Loops = 4
f4 =4(f1)

5. Standing Waves - Strings
With the fundamental AND harmonics sounding at the same time, the wave looks like….
cello

6. Standing Waves - Strings
Frequencies for standing waves:
n = number of the harmonic
L = Length of the vibrating string
v = velocity of a string
*Different notes are achieved by changing the length of the vibrating string.

7. Example 11
A violin string is under a force of tension of 87.0 N. The vibrating portion of the string is 32.0 cm long and has a mass of 0.35 g. The string begins vibrating, creating a fundamental frequency.
What is the velocity if this string under such conditions?
What is the fundamental frequency produced?
What are the values of the second and third harmonics for this fundamental?

8. Example 12
A string of length 0.26 m is fixed at both ends. The string is plucked and a standing wave is set up that is noticeably vibrating at its second harmonic. The traveling waves that make up the standing wave have a speed of 155 m/s. What is the frequency of vibration?

9. Standing Waves – Woodwinds and Brass
These instruments create standing waves using vibrating columns of air
Two Categories:
Instruments (Pipes) Open at Both Ends
All brass instruments, flute, organ
Instruments (Pipes) Open at One End
Most reed and double-reed instruments: Clarinet, Oboe, Saxophone, Bassoon, etc..

10. Standing Waves – Pipes Open at Both Ends
*Standing waves have nodes and anti-nodes. The part that can create sounds (vibrations) is the
anti-node
*Need an anti-node at both ends
Fundamental
1st Harmonic
2nd Harmonic
3rd Harmonic
4th Harmonic

11. Standing Waves – Pipes Open at Both Ends
Frequencies for standing waves:
n = number of the harmonic
L = Length of the vibrating column of air
**v = velocity of sound in air (343 m/s)
*Different notes are achieved by changing the length of the vibrating column of air