Resonance

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.

Assessment 1.Why do you hear different notes when you tap on different types of drinking glasses? 1.Which is NOT an example of resonance? A.a person pushing a child higher and higher on a swing B.a child bouncing a ball up and down C.a singer singing a specific note, causing a glass to vibrate and break D.a trumpet player vibrating his lips to play a note

Physics terms oscillation amplitude frequency natural frequency periodic periodic force resonance

Natural frequency The frequency at which a system tends to oscillate is called its natural frequency. animated illustration, page 398

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. Each string on a guitar oscillates with a different natural frequency. Natural frequency The frequency at which a system tends to oscillate is called its natural frequency.

Brainstorm with a partner: What factors do you think affect the natural frequency of a vibrating guitar string? Hint: there are two important factors. Natural frequency

More inertia: lower frequency

Stronger restoring force: higher frequency

When playing a guitar, how do you increase the inertia to play a lower frequency note? Test your knowledge

When playing a guitar, how do you increase the inertia to play a lower frequency note? use one of the thicker, heavier strings How do you increase the restoring force to play a higher frequency note?

Test your knowledge When playing a guitar, how do you increase the inertia to play a lower frequency note? use one of the thicker, heavier strings How do you increase the restoring force to play a higher frequency note? tighten the string

In Investigation 14C you will measure the natural frequency of a mass on a vertical spring. The investigation is found on page 402. Investigation

1.Set up the mass hanging from the spring. Mount the spring to a lever and post attached to the stand. 2.Attach a ruler to the stand, centered on the hanging mass. 3.Pull the mass down slightly to start it oscillating. 4.Measure the time for 10 oscillations. Part 1: Find the natural frequency Investigation

a.What is meant by the oscillator's “natural frequency”? b.What are the values of your oscillator's natural period and frequency? Investigation Questions for Part 1

Investigation Part 2: Creating resonance 1.Set the timer to beep at a frequency of between 0.1 and 3 Hz. 2.Use one hand to hold the stand in place. Use your other hand to press down on the lever on each beep. 3.Have your partner estimate the amplitude of the motion using the ruler.

Investigation 4.Measure the oscillation amplitude for at least ten frequencies between 0.1 Hz and three times the natural frequency. 4.Graph the oscillation amplitude versus the frequency of the periodic force. Part 2: Creating resonance

a.Define resonance by referring to the motion you just observed and the graph of your data. b.At what frequencies is the oscillator in resonance? out of resonance? c.Describe the flow and storage of energy in the system at resonance. Investigation Questions for Part 2

A periodic force is repeated in cycles: push – wait – push - wait Periodic forces

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

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

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

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

You found the resonant frequency of a spring mass system experimentally. There also an equation for the resonant frequency of a spring mass system. What variables do you think the frequency depends on? (Hint: What two factors did we talk about earlier?) 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 Mass and spring system

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. Mass and spring system

Pendulums also have a natural frequency and period: Pendulums

Assessment 1.Why do you hear different notes when you tap on different types of drinking glasses?

Assessment 1.Why do you hear different notes when you tap on different types of drinking glasses? The drinking glasses each have a different natural frequency. When you strike them, they vibrate at their natural frequency, creating a sound wave that you hear.

Assessment 2.Which is NOT an example of resonance? A.a person pushing a child higher and higher on a swing B.a child bouncing a ball up and down C.a singer singing a specific note, causing a glass to vibrate and break D.a trumpet player vibrating his lips to play a note

Assessment 2.Which is NOT an example of resonance? A.a person pushing a child higher and higher on a swing B.a child bouncing a ball up and down C.a singer singing a specific note, causing a glass to vibrate and break D.a trumpet player vibrating his lips to play a note