1. 11/25 Standing Waves (for Lab)
Today: Angular Momentum Demos
HW “Angular Momentum” Due Wednesday 12/4 Follow instructions on handout
Class canceled 12/2

2. Standing Waves: Only happen at certain frequencies
Resonance phenomenon
NODES: points of zero vibration
ANTINODES: points of maximum vibration
Made of two waves moving in opposite directions-we can use v = f

3. Snapshot L
What is the wavelength?

4. L
l =
2/3 L
What is the wavelength?

5. L
l =
2/3 L
What is the wavelength?

6. L
l = L
What is the wavelength?

7. L
l =
2 L

8. L
l =
2 L

9. Problem
The string has a length L and pulses travel at speed v. At what frequency must I “drive” it to produce
a. the fundamental? (call this f1)
b. the second harmonic? (call this f2)
c. the third harmonic? (call this f3)
Important point: we get integer multiples of the fundamental.

11. a. Draw a picture of the standing wave pattern.
A string stretched between 2 fixed supports sets up standing waves with 2 nodes between the ends when driven at 240 Hz.
a. Draw a picture of the standing wave pattern.
b. What is the fundamental frequency?
c. At what frequency will the standing wave have 3 nodes between the ends?

13. Standing Waves:
Transverse: v = f 
Longitudinal: v = f 

14. Organ Pipes: 2 Types 1 = 2L 1 = 4L Open Pipe (open on both ends)
f1 = v/2L A A
Closed Pipe (one open, one closed end)
1 = 4L N
f1 = v/4L A

15. Open Organ Pipe 1 = 2L f1 2 = L 2f1 3 = 2/3 L 3f1 f1 = v/2L

16. Closed Organ Pipe
1 = 4L f1
f1 = v/4L N A
? = 4/3 L
3f1
f? = 3v/4L

17. Closed Organ Pipe 1 = 4L f1 f1 = v/4L 3 = 4/3 L 3f1 f3 = 3v/4L

18. Resonant Structure For Strings:
All multiples of f1: (f1, 2f1, 3f1, 4f1…)
For Pipes-both ends open:
For Pipes-one end open, one closed:
Odd multiples of f1: (f1, 3f1, 5f1, 7f1…) Even multiples missing