Do Now (2/3/14):Do Now (2/3/14):

*Pass in your homework

1. What is a wave?

2. What are some characteristics of waves?

3. What are some different types of waves?

4. What are some quantities that are associated with waves?

ObjectivesObjectives

Discuss the origin and significance of beats.Solve problems using propagation speed,

frequency, and wavelength.Use the superposition principle and

determine the resultant wave when two waves merge.

Understand the principles of reflection, refraction, dispersion, and diffraction as they relate to mechanical waves.

Wave basicsWave basics

Transverse vs longitudinalStanding wavePeriodFrequencyAmplitudeIntensity v=fNode, antinode

Standing WavesStanding Waves

Standing waves are produced when waves traveling in opposite directions overlap– When they overlap

they add to each other– Positive parts of the

waves get bigger; negative parts subtract

InterferenceInterference

Waves will interact in space.

Constructive and destructive interference. Depends upon the phase relationship between the waves.

Video…

Waves Add When They Overlap

Another simulation

Natural FrequenciesNatural Frequencies

When any object composed of elastic materials is disturbed, it vibrates at its own set of frequencies.– We call these an object’s natural frequencies.

Natural frequency Natural frequency

The frequency that requires the minimum energy to produce forced vibrations. This is also the frequency that requires the least amount of energy to continue this vibration.

The natural frequency depends on the elasticity and shape of the object.

ResonanceResonanceNatural frequency of vibration.Forced vibration near or equal to natural

frequency results in high amplitude.Significance to solid objects.

Tuning ForksSinging wine glassWater in a tube.Tacoma Narrows in 1940.

ProblemProblem

A sound wave in air has a frequency of 262 Hz and travels with a speed of 330m/s. How far apart are the wave crests (compressions)?

Sound is a longitudinal waveSound is a longitudinal wave

Sound can also be called a Sound can also be called a pressure wave pressure wave

Humans hear 20-20,000 hzHumans hear 20-20,000 hz

Pitch vs frequency

Speed of sound is 331m/s @ 0°C. Add .6m/s for every additional degree.

When Sounds Are Close in When Sounds Are Close in Frequency We Hear BeatsFrequency We Hear Beats

Beat frequency Beat frequency

:

21 ff

PracticePractice

How many beats per minute are heard when two strings of a guitar are played, where the D string has a frequency of 330 Hz and the B string has a frequency of 247 Hz?

Intensity and AmplitudeIntensity and AmplitudeLoudness is the impression of sound

intensity.Intensity is the energy transported by a

wave per unit of time across unit area.Decibel combines “loudness” and intensity

using logarithmic scale. (in dB) = 10log(I/I0)

I is proportional to 1/r2

Doppler EffectDoppler Effect

Occurs with all waves when either the source and/or the observer are moving relative to the other.

http://www.surendranath.org/applets/waves/doppler/dopplerapplet.html

http://www.kettering.edu/~drussell/Demos/doppler/doppler.html

The Doppler Effect The Doppler Effect Equation: (o=observer, s =source

What would the equation be for a stationary observer?

s

o

vv

vvff '

Do Now (2/4/14):Do Now (2/4/14):

A tuning fork produces a steady 400Hz tone. When it is struck and held near a vibrating guitar string, twenty beats are counted in five seconds. What are the possible frequencies produced by the guitar string?

Doppler Effect – Stationary Doppler Effect – Stationary Observer Observer

Doppler FrequenciesDoppler Frequencies

Doppler Effect PracticeDoppler Effect Practice

Two automobiles are equipped with the same single-frequency horn. When one is at rest and the other is moving toward an observer at 15m/s, a beat frequency of 5.5 Hz is heard. What is the frequency the horns emit? Assume 20°C.

Practice:Practice:

Work with your group to complete the multiple choice questions in chapter 14. This will be collected!

Do not forget to justify each of your answers!!!!

More sound infoMore sound info

Air columns

– Open column L=1/2λ

– Closed column L=1/4λ

Calculating HarmonicsCalculating Harmonics

Slinky LABSlinky LAB

Do Now (2/5/14):Do Now (2/5/14):

A train moving at a speed of 40 m/s sounds its whistle, which has a frequency of 500 HZ. Determine the frequency heard by a stationary observer as the train approaches the observer. (use 345 m/s for the speed of sound)

A cylindrical air column with both ends open will vibrate A cylindrical air column with both ends open will vibrate with a fundamental mode such that the air column length with a fundamental mode such that the air column length is one half the wavelength of the sound wave. Each end is one half the wavelength of the sound wave. Each end of the column must be an antinode for the airof the column must be an antinode for the air

Open Pipe Harmonics Open Pipe Harmonics

Air Particles:Air Particles:

Closed Pipe HarmonicsClosed Pipe HarmonicsA closed cylindrical air column will produce

resonant standing waves at a fundamental frequency and at odd harmonics.

The closed end is constrained to be a node of the wave and the open end is an antinode.

In the fundamental mode the wavelength is four times the length of the air column.

The closed end prevents the column from producing the even harmonics.

Closed Pipe Harmonics Closed Pipe Harmonics

Practice:Practice:

A pipe is 2.46 m long. Determine the frequencies of the first three harmonics if the pipe is open at both ends. Take 345 m/s as the speed of sound in air.

Harmonic practiceHarmonic practice

What will be the fundamental frequency and first 2 harmonics for a 40cm long organ pipe at 20° C if it is open?

What about if it is closed?

PracticePractice

A pipe in air at 20°C is to be designed to produce two successive harmonics at 240Hz and 280Hz. How long must the pipe be, and is it open or closed?

Misc Sound notesMisc Sound notes

Reflection

Refraction

Dispersion

Diffraction

Reflection - Waves Will Reflect Reflection - Waves Will Reflect When They “Bounce” Off of an When They “Bounce” Off of an

Object Object

What do you notice about the reflected wave compared with the starting wave?

Refraction:  The Bending of Refraction:  The Bending of Wavefronts Wavefronts

The wave front bends because of a difference in the velocity of the wave due to material change.

Waves Also Spread Out (Diffract) Waves Also Spread Out (Diffract) When They Go Through Openings or When They Go Through Openings or

Around ObjectsAround Objects

Do Now (2/6/14):Do Now (2/6/14):

What will be the fundamental frequency and first 2 harmonics for a 40cm long organ pipe at 20° C if it is open?

What about if it is closed?

Practice:Practice:

Complete the Refraction Worksheet*Bonus: complete as many multiple

choice problems from chapters 14 and 20 as you can – do not forget to justify your answers!!!

Or you may work on your homework

Do Now (2/7/14):Do Now (2/7/14):After passing from one material into

another, a light ray makes an angle of refraction of 11.63º. If it came from a medium with index of refraction 1.74 and passed into a medium with index of refraction 1.35, what angle of incidence did the ray make when it was in the first medium?

InvestigateInvestigate

You have three things to work on. Take turns:

1. tuning fork investigation2. Waves at Boundaries Investigation3. AP Problem (part ii is tricky! Don’t

worry about it if you can’t solve)

Videos Videos

http://www.acs.psu.edu/drussell/Demos/reflect/reflect.html

http://www.animations.physics.unsw.edu.au/jw/waves_superposition_reflection.htm

Electromagnetic SpectrumElectromagnetic Spectrum

Who is Maxwell and what are his equations?

Electromagnetic WavesElectromagnetic Waves

Accelerating electrical charges produce magnetic fields that produce electric fields etc. http://micro.magnet.fsu.edu/primer/java/wavebasics/index.html

Propagate away from source in form of transverse wave.

Energy that can travel through space. 3.0 x 108 m/s

Electromagnetic SpectrumElectromagnetic Spectrum

Classifies e-m energy according to frequency.

All travel at same speed in vacuum.c=fhttp://micro.magnet.fsu.edu/primer/java/

wavebasics/index.html

Electromagnetic SpectrumElectromagnetic Spectrum