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A kid is swinging on a swing with a period T. A second kid climbs on next to the first, doubling the weight on the swing. The period of the swing is now... A) the same, TB) 2TC) D) none of these.

Clicker Question Room Frequency BA

2T

The period of a simple pendulum does not depend on the mass

T =2π Lg

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• FCQs for the course will be administered Friday, Dec 2nd

• CAPA assignment #14 is due on Friday at 10 pm.

• This week in Section: Lab #6 (with prelab)

• Next week: Review in Section, Make-up Labs arranged in other sections. Contact your TA this week to arrange a make-up lab. Last chance to make up labs! 5 labs must be completed in order to pass this course.

• Detailed Reading Assignments:– Sections 11.1-11.4, 11.7-11.9,11.11-11.13

– Sections 12.1-12.4, 12.7-12.8

– Sections 13.1,13.2, 13.6-13.10

– Sections 14.1-14.5

Announcements

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• Final Exam is Tuesday morning, Dec 13, 10:30am – 1pm

• Exam will be held in Coors Event Center, more details next week

• Practice Exams and Formula sheet will be posted on Monday Dec 5th

• Prof. Nagle will hold a review session on Thursday evening, Dec 8th, 7-9pm, in this room (Duane G1B30).

• Exam coverage is cumulative!

Final Exam News

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Wave Basics – Taxonomy ITwo Basic Types: Impulse and Periodic

vImpulse on Rope

Periodic on Rope v

Sinusoidal on Rope v

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Transverse Wave

LongitudinalWave

Wave Basics – Taxonomy IITwo types of Wave Motion of Medium: Longitudinal and Transverse

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Wave Examples

Some common examples of waves are• Sound waves (pressure waves) in air (or in any gas or solid or liquid) – Longitudinal in gas/liquid, both transverse and longitudinal in solid• Waves on a stretched string – Transverse• Waves on a slinky – Transverse and Longitudinal• Waves on the surface of water - Transverse and Longitudinal• "The Wave" at the ballpark stadium. The medium is the people – Transverse• Electromagnetic waves (light) – this is the only kind of wave which does not require a medium! Their properties indicate they are transverse, but you’ll learn more on EM waves next semester.

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The graph below shows a snapshot of a wave on a string which is traveling to the right. There is a bit of paint on the string at point P.

At the instant shown, the velocity of paint point P has which direction?

E) None of these

Clicker Question Room Frequency BA

y

x

P

vwave

v

x

y

8

The graph below shows a snapshot of a wave on a string which is traveling to the right. There is a bit of paint on the string at point P.

At the instant shown, the acceleration of paint point P has which direction?

E) None of these

Clicker Question Room Frequency BA

y

x

P

vwave

v

x

y

Steep slope on the wave form means high velocity of paint point, slope in getting larger in magnitude

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Description of Periodic Waves

All waves move through medium with a speed v which is characteristic of the medium, and this is related to λ and T:

Periodic waves are described in terms of three basic quantities:Wavelength λ, Period T, and amplitude A:

vλ

Period T for one piece of medium to complete a motion cycle

v=λT

It take time T for the wave to travel distance λ:

2A

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Frequency and Wave Number Periodic Waves

A new inverse quantity is the wave number k = 2π/λ.Long wavelength λ gives small wave number k.

We can use inverse quantities to describe periodic waves: Frequency f = 1/T so we can also write: v = λfAngular Frequency ω = 2π/T = 2πf so we can write : v = λω/2π

vλ

Period T for one piece of medium to complete a motion cycle

v=2πkT

We now can write three more relations: v=2π fk

v=ωk

Always check units!!!

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Wave speeds

In most cases, the wave speed v does NOT depend on f or λ; it just depends the type of medium and how it is excited.

This immediately implies that since v =λf, and v is constant, then large λ corresponds to small f and small λ corresponds to high f.

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Three waves are traveling along identical strings (same mass per length, same tension, same everything). Wave B has twice the amplitude of the other two. Wave C has 1/2 the wavelength than A or B. Which Wave goes slowest? A B C D) All have same v

Clicker Question Room Frequency BA

Identical string conditions give identical v

y

x

vwave

y

x

y

x

A

C

B

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Three waves are traveling along identical strings (same mass per length, same tension, same everything). Wave B has twice the amplitude of the other two. Wave C has 1/2 the wavelength than A or B. Which wave has the highest frequency? A B C D) All have same f

Clicker Question Room Frequency BA

Smallest wavelength λ gives highest frequency f

y

x

vwave

y

x

y

x

A

C

B

v=λ f

No dependence on amplitude

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Wave InterferenceSuperposition Principle: If two or more waves are present in the same place, at the same time, the total wave is the sum of the individual waves: ytot(x,t) = y1(x,t) + y2(x,t). You get constructive or destructive interference depending on whether y1 and y2 add (both have same sign) or cancel (opposite signs).

We can see this in the simuation

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Standing WavesTwo sinusoidal traveling waves of the same λ (and therefore the same f = v/λ ) and the same amplitude, traveling in opposite directions, overlapping in the same region of space, make a standing wave.

mx

nodes anti-nodes

λends fixed

L

We can see this in both the simulation and a rope!

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A string is clamped at both ends and then plucked so that it vibrates in a standing mode between two extreme positions A and C. Let upward motion correspond to positive velocities. When the string is in position B, the instantaneous velocity of points along the string is…

A) zero everywhere. B) positive everywhere.C) negative everywhere. D) depends on the position.

Clicker Question Room Frequency BA

No dependence on amplitude

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Wave Simulations

http://phet.colorado.edu/en/simulation/wave-on-a-string