1. Standing waves
– Fundamental frequency
– What is it?
– Which harmonic?
How can you find wavelength?
Harmonics
v= fλ
v
f =
λ How do you know that the
wavelength is equal to 2L?
v
f =
2L

2. What is the
Wavelength?

3. Strings & Open Pipes
Nodes & antinodes
2L v v nv
λ= fn = = =
Harmonics
n λ 2L 2L
–What is n? n
–What numbers can it be?
A N A
A A A
N N
A N A A A
N N

4. On Closed Pipes v v nv
4L fn = = =
λ= λ  4L  4L
n  ÷
 n 
Harmonics
–What is n?
–What numbers can it be?
A N
A A N
N
A A A
N N N

5. Why do instruments have different sound
even if they play the same note?
– Overtones
Different relative intensities of different
harmonics
Timbre
440 Hz
880 Hz
Mixed

6. Factory Whistle
Soprano
Piano

7. Factory Whistle
Soprano
Piano