1. Resonance

2. Objectives
Examine and describe how waves propagate in oscillatory systems.
Investigate wave interference in an oscillating system.
Investigate the phenomenon of resonance in an oscillating system.

3. Physics terms oscillation amplitude frequency natural frequency
periodic
periodic force
resonance

4. Equations
Pendulums
Springs

5. Natural frequency
The frequency at which a system tends to oscillate is called its natural frequency.
Each string on a guitar oscillates with a different natural frequency.
A guitar string that plays the note middle C has been tuned to have a natural frequency of 262 Hz.

6. More inertia: lower frequency
NOTES

7. Stronger restoring force: higher frequency
NOTES

8. Test your knowledge
When playing a guitar, how do you increase the inertia to play a lower frequency note?
How do you increase the restoring force to play a higher frequency note?

9. Resonance
NOTES
Resonance occurs when the periodic force is applied at the natural frequency.

10. Condition for resonance
NOTES
If the frequency of the periodic force is EQUAL to the natural frequency, you have resonance.

11. No resonance
NOTES
If the frequency of the periodic force is NOT EQUAL to the natural frequency there is NO resonance.

12. Resonance and energy
The energy of the resonant system increases with each application of the periodic force.

13. Mass and spring system The resonant frequency depends on:
the strength of the spring force, which increases with k
the inertia, which is the mass, m

14. Mass and spring system NOTES Here’s the equation, and it makes sense:
As k increases (and the restoring force increases) the natural frequency goes UP.
As the mass m increases, the natural frequency goes DOWN.

15. Pendulums
NOTES
Pendulums also have a natural frequency and period:

16. Assessment
Why do you hear different notes when you tap on different types of drinking glasses?

17. Assessment Which is NOT an example of resonance?
a person pushing a child higher and higher on a swing
a child bouncing a ball up and down
a singer singing a specific note, causing a glass to vibrate and break
a trumpet player vibrating his lips to play a note