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?
Objectives

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 basics

Transverse vs longitudinal
 Standing wave
 Period
 Frequency
 Amplitude
 Intensity
 v=f
 Node, antinode
Standing 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
Interference

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 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

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.
Resonance

Natural frequency of vibration.
 Forced vibration near or equal to natural
frequency results in high amplitude.
 Significance to solid objects.

Tuning Forks
 Singing wine glass
 Water in a tube.
 Tacoma Narrows in 1940.
Problem

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 wave
Sound can also be called a
pressure wave
Humans 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
Frequency We Hear Beats
Beat frequency

:
f1  f 2
Practice

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 Amplitude

Loudness 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 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

Equation: (o=observer, s =source
 v  vo 

f '  f 
v

v
s 


What would the equation be for a stationary
observer?
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
Observer
Doppler Frequencies
Doppler 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:

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 info

Air columns
– Open column
L=1/2λ
– Closed column L=1/4λ
Calculating Harmonics
Slinky LAB
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
with a fundamental mode such that the air column length
is one half the wavelength of the sound wave. Each end
of the column must be an antinode for the air
Open Pipe Harmonics
Air Particles:
Closed Pipe Harmonics

A 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
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 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?
Practice

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 notes

Reflection

Refraction

Dispersion

Diffraction
Reflection - Waves Will Reflect
When They “Bounce” Off of an
Object
What do you notice about the reflected wave compared
with the starting wave?
Refraction: The Bending of
Wavefronts
The wave front bends because of a difference in the
velocity of the wave due to material change.
Waves Also Spread Out (Diffract)
When They Go Through Openings or
Around Objects
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:

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):
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?
Investigate

You have three things to work on. Take
turns:
 1. tuning fork investigation
 2. Waves at Boundaries Investigation
 3. AP Problem (part ii is tricky! Don’t
worry about it if you can’t solve)
Videos

http://www.acs.psu.edu/drussell/Demos/refl
ect/reflect.html
 http://www.animations.physics.unsw.edu.au
/jw/waves_superposition_reflection.htm
Electromagnetic Spectrum

Who is Maxwell and what are his
equations?
Electromagnetic Waves


Accelerating electrical charges produce magnetic
fields that produce electric fields etc.
http://micro.magnet.fsu.edu/primer/java/wavebasi
cs/index.html
Propagate away from source in form of transverse
wave.
 Energy that can travel through space.
 3.0 x 108 m/s
Electromagnetic Spectrum

Classifies e-m energy according to
frequency.
 All travel at same speed in vacuum.
 c=f
 http://micro.magnet.fsu.edu/primer/java/wa
vebasics/index.html
Electromagnetic Spectrum