1. Resonance And Other Stuff.
Lecture 9
Resonance
And Other
Stuff.

2. Last Time
We looked at springs and noted that the big masses on springs had a lower frequency and a longer period than lower masses.
We also found that the STIFFER (larger K) springs had a higher frequency

3. Two Spring Mini-Demo 01

4. K K K/2

5. Let’s Look at a “Springy String”
DEMO-02

6. The Tones f0

7. The FIFTH (???)
DOES A STRING REALLY VIBRATE THIS WAY???

8. Take a look f0 is the first tone. The octave is 2f0.
The NEXT octave is 4f0.
The NEXT octave is 8f0.
DOUBLE FOR EACH OCTAVE

9. Another Perspective f0 2f0 4f0 8f0 octave Next octave 3f0 (3/2)f0
fifth

10. Surprised? The octave interval sounds good to us…
The frequency is a double of it.
Let’s look at the curve.

11. The Pressure Waves at the EAR
Louder
Softer

12. More pressure
Low tone
Higher tone

13. f and 2f – The Octave www.polyphonicstudios.editme.com/ musicbasics
Same basic period! A
A + A’ A’
musicbasics

14. Octave tones + Fifth
period

15. Back to RESONANCE
Most objects have a “natural frequency” at which they will oscillate.
Think of a swing … you have to push it at just the right moment for it to increase in height.
We are applying a force at the “RIGHT FREQUENCY” … the RESONANT FREQUENCY.
The “natural frequency” of oscillation of an object is also the RESONANT REFQUENCY

16. The Resonant Driven Spring
DEMO 04
The Resonant Driven Spring

17. This works for many objects … including bridges
DEMO 05
VIDEO Tacoma Narrows Bridge

18. WHY DOES A STEADY WIND CAUSE A VIBRATION???
Bridge “model”
Spring Action
From the supports

19. WHY DOES A STEADY WIND CAUSE A VIBRATION???
Bridge “model”
Spring Action
From the supports
Wind Shift

20. WHY DOES A STEADY WIND CAUSE A VIBRATION???
Bridge Tries to
Restore.
WIND
Bridge “model”
Spring Action
From the supports
Wind Shift

21. WHY DOES A STEADY WIND CAUSE A VIBRATION???
Bridge Tries to
Restore.
WIND
Supports
Bridge “model”
Spring Action
From the supports
Wind Shifts
back
The bridge oscillates at its natural (resonant) frequency
while on each cycle the approximately horizontal wind
provides it an additional push at just the right moment!

22. Remember this effect
for when we look at
woodwind instruments.

23. What to Read?? Bolemon Johnston Chapter 16 pages 300-301, 305
We will fill in the “energy gap next”.
Johnston
Chapters 2 and 3. Skip the interlude for now.
Read the section on energy as a good introduction to the subject.