33 - Resonance

# 33 - Resonance - Longitudinal Standing Waves For next time...

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Longitudinal Longitudinal Standing Waves Standing Waves For next time: HW: handout, problems 7, 8, & 9

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vf λ = Summary 1 1 1 1 2 f L v v f = = = 1 1 2 3 1 4 1 1 2 11 2 2 2 2 3 2 4 3 4 L L L L == 2 2 1 2 2 2 vv f L f == = 3 3 1 3 2 3 f L f 41 4 4 2 4 f L f

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Problem One end of a hacksaw blade is clamped to a post. The other end is free. Draw graphs showing the two lowest harmonics that can occur on the hacksaw blade. What is the wavelength of each harmonic in comparison to the length L of the blade?
Hacksaw blade NA NN AA 4 L λ ⇒= 1 4 L = fundamental 3 4 L = 4 3 L third harmonic

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Which harmonics resonate? ± Ends are the same: Multiples of f 1 : f 1 , 2f 1 ,3f 1 , 4f 1 ± Ends are different: Odd multiples of f 1 : f 1 , 3f 1 , 5f 1 , 7f 1 ...
Longitudinal standing waves

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Standing waves Transverse: v = λ f Longitudinal: v = f
Longitudinal standing waves

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Longitudinal standing waves
Longitudinal standing waves C

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Longitudinal standing waves CD
Longitudinal standing waves CDC

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Longitudinal standing waves CDCD
Longitudinal standing waves

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Longitudinal standing waves DCDC
Longitudinal standing waves DCDC

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Longitudinal standing waves
Longitudinal standing waves

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Longitudinal standing waves
Make it sing!

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33 - Resonance - Longitudinal Standing Waves For next time...

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