Mr. DelGiudice
Honors Physics
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Define what wavelength and amplitude of a wave are and draw a picture of them.
How do we define the frequency (of a wave)?
What formula relates all of them?
How does the speed of sound vary with temperature?
Is the speed of a wave faster in a solid liquid or a gas? Why?
What kind of wave is a sound wave? Longitudinal or Transverse.
Your objective by the end of class: Be able to
 What are sound waves and how are they produced?
 Describe what is a standing sound wave and how they differ
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from each other.
Describe what are harmonic frequencies and how do we
visualize them through nodes and anti node diagrams
Calculate simple fundamental harmonic frequencies for
Demonstrate that physics laws govern harmonic
frequencies for stringed instruments or open ended ended
instruments . How do laws predict what frequencies an
instrument can produce?
Do all instruments give the same harmonic frequencies?
Frequencies Video
What is a Standing Wave?
What are their characteristics?
• A Standing wave is a wave produced by
superposition of two periodic waves having
identical frequencies and amplitudes which travel
in opposite directions.
•In a stringed instrument , the standing wave is
produced by waves reflecting off a fixed end and
interfering with the oncoming waves as the wave
travels back through the medium..
•In an opened end instrument , compressions and
rarefactions cause the interference patterns..
Closed at one end have a mixture of both of the above
interference patterns.
How are sound waves produced?
Sounds are produced by vibrations
Being a longitudinal standing wave , sound
waves are characterized by regions of
compressions ( condensation)and expansions(
rarefactions) as they moves through a medium.
What are Sound standing wave
characteristics
Sounds …….
 are produced by vibrations
 being longitudinal waves it is characterized by
regions of compressions ( condensation)and
expansions( rarefactions) as it moves through a
medium
 are defined by frequency in Hz, wavelength in
meters and velocity in(m/s).
 Pitch refers the frequency of sound in Hertz( Hz)
What is a Standing Sound wave
again?
A Sound wave
 Is a movement of a wave causing compressions and
expansions of molecules longitudinally.
 It’s source is that of simple harmonic motion
 It has a fundamental frequency, f ; a wavelength , ʎ and a
velocity, v
 It is represented by a standing wave and can produce
harmonic frequencies predicted by physics laws.
 Can move through mediums at different speeds.
speed of sound through air @ 0 C is 331 m/s
Has a fixed velocity, wavelength and speed.
 Can be measured for these characteristics
Nodes and antinodes describe
allowable frequencies
Nodes and anti nodes Make up
standing waves
Nodes and Anti nodes and their drawings
Node : A point on the wave of minimal disturbance
Anti Node : A point on the wave where there is
maximum disturbance
What are harmonic frequencies?
 Demo.. Alex, Alexie , Dawn Guitar
 Del : Clarinet , Guitar ,Harmonica
Listen to the harmonic sounds..
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Guitars E note
Harmonica E
Tuning fork E
Piccolo or flute if present
Which has a higher pitch or frequency?
How are they related?
Physics helps us to predict they are related?
Lets look at what is harmonics?
Octaves are pairs of the Harmonic frequency Series
Harmonic of a fundamental frequency
The 1st harmonic and
the 2nd harmonic frequencies
are considered an octave apart.
n= 1 C 256 Hz = f1
n= 2 C 512 Hz = 2 ∙ f1
n= 3 C 768 HZ = 3 F1
And so on
?
Harmonic frequencies
what are they?
What physics laws predict
them?
Harmonic
Frequencies
How are sound waves produced
again?
 Listen to the instruments .
 DR D .. Alex , Alexie, Dawn others?
 Answers??
How do Vibrating Strings or
Vibrating Air Columns produce
sounds of different frequencies?
How Physics help predict
which instruments have high
or low frequencies of sounds?
What are nodes and anti nodes aga
They represent maximum and
minimum????????? Amplitudes!!
Nodes and anti Nodes
For Open end or Stringed
Closed at one end
 Displacement anti nodes at
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both ends
Must have at le have at least
one length to have wave at all.
Single node corresponds to f1.
L = 1/2λ or λ = 2L
fn = n v/2L v = speed of sound in air
F n=2 = 2 v/2L= v/L λ = 2L
All integers allowable n=
1,2,3…… ex flute
Displacement node always at
closed end
Anti node at open end
L = λ/4( ½ that of open end)
Odd harmonics n= 1,3,5,7
only allowed
 Chang L or diameter get
different sound
 Ex Clarinet closed end
 Longer L lower f
f
Sample Problem using Harmonic equation for Frequency.
Q1. What is the first harmonic frequency ( for n=1,) in a 2.5 meter long
pipe that is open at both ends ? Assume speed of sound in air is 345
m/s?
f1 =
Q2. What is the fundamental frequency f1, a Guitar string when the
speed of waves on the string is 115 m/s and the effective string length is
25 cm( 0.25m) ?
f1 =
Sample Problem using Harmonic equation for Frequency.
Q1. What are the first harmonic frequencies ( for n=1 ) in a 2.5 meter
long pipe that is open at both ends ? Assume speed of sound in air is
345 m/s?
f1 =
Ans = 69 Hz
Q2. What is the fundamental frequency of a Guitar string when the
speed of waves on the string is 115 m/s and the effective string length is
25 cm( 0.25m) ?
Ans= 230Hz
Challenge!!! Go for it!!!!!!
Prize Time!!!!! By end of class
What would be the fundamental frequency and t he first overtone
For a 26 cm long organ pipe at 343m/s velocity ( 20 Celsius) if it is
a) Opened at both ends n = ? , n= ?
b) Closed at one end n= ? , n= ?
String Lengths
For the stringed or open ended
harmonic frequencies
n=1
ʎ 1= 2 L
n=2
ʎ 2= L
n=3
ʎ2= 2L/3
n=4
ʎ2= 1L/2
F1
2 F1 = F 2
3 F1 = F 3
4 F1 = F 4
How many antinodes and
nodes are there for the
nd
3 harmonic frequency? For
th
the 5 ?
Now can we measure Harmonic
Frequencies? How?
Open-end or stringed
harmonic frequency formula
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f ∙ʎ = v frequency times
wavelength = velocity
 Since for an open ended pipe or stringed
instrument :
f = v
since ʎ = 2L
ʎ
here L is length in m
f = v
for fundamental frequency
2L
For Closed at one end pipes
frequencies are odd!
f ∙ʎ = v frequency times
wavelength = velocity
 Since for an closed ended pipe
instrument
 since ʎ = 4L here L is length in m
v
since ʎ = 4L
ʎ
here L is length in m
 f = (n) v
for fundamental frequencies
f =
4L
n = 1,3,5,7, only odds
Check for understanding time..
Using the Frequency Harmonic motion equation for open ended or stringed
instruments:
f = n• v/2L where n = 1 for fundamental and n= 2,3,4,5 for harmonic series
Q1. What is the first harmonic frequency ( for n=1) for a wave in a 2.5 meter long
pipe that is open at both ends ? Assume speed of sound in air is 345 m/s?
Q2. What is the fundamental frequency of a Guitar string when the speed of waves
on the string is 115 m/s and the effective string length is 62.5 cm( 0.625m) ?
Look at hand out:
Harmonics for AP
Music/Physics Theory!!
Listening?
String Measurement
Can You Measure Harmonic
Frequencies of Instruments ?
 Go to station 1 or 2 or 3 or 4
 Work with your group to answer the work station
questions given the problem shown
 Be sure to write your answers on the sheet provided and
show /draw any diagrams and show work for any
calculations asked for.
 Be sure to discuss your answers among your group and
elect one spokesperson for each group to report back
out once the activity is completed and we are back at
Work Station 1
Can you measure the fundamental frequency( n=1) of a flute with all holes closed?
Step 1 : Use the flute in front of you. Using a meter stick and measure the actual
length of the flute from the center of the ligature (mouth opening) to the longest end
of the flute in cm. record the findings in cm and then change to meters to get the
experimental length.
Experimental length by measurement=
____________ cm ==
________________m
A flute is designed so that is plays a frequency (f ) when all the holes are covered the
temperature is @20 Celsius ( v sound = 343 m/s)
Step 2 : Consider the flute to be an opened at both ends pipe. Find the theoretical
Length L of the flute assuming the fundamental frequency n = 1, assuming that the C
frequency of 264 Hz is the fundamental frequency. Assume frequency = v /
wavelength and wavelength = 2 x L
So f = (n) v / 2L
solve for L
Where f is frequency and v is velocity of sound and L is length to be calculated. n=1
Work Station 2.
Sound and the Guitar ( stringed instrument )
The thickest string on the guitar is strung from the nut to the bridge .
Some electric guitars measure 0.63 m from nut to bridge for the E or
thickest string and has harmonic frequency, f 1, when pressing on the first
fret of 329 Hz.
For your guitar workstation , put your finger on the first fret and measure
from the point you press on the string (middle of fret 1 )to the bridge in
cm.
Change the measurement to meters ..
Assume frequency = v / wavelength and wavelength = 2 x L
So f = (n) v / 2L
solve for L assume n= 1
Record this measurement, in ___ cm then change to __ meters
Assuming you have a stringed instrument, f = v/2L Assume v = 343m/s
in the room then calculate L in cm then m
WORK STATION 3
Problem SOLVING!
Go to work station #3 and problem solve
Work individually and collectively as a
group! Get the correct answers show all
work!
Work Station # 4
YOU’RE A NODE!!!! Or An ANTI_NODE???
Physics NODES and Anti –NODES
Try to decipher the patterns and draw logical
infer ances and answers!! HA HA
Please Answer Questions Correctly…
Look at hand out:
Harmonics for
Theory
It’s the end of class: Are you able to…..
 Describes what are sound waves and how are they
produced?
 Describe what is a standing sound wave and how they differ
from each other.
 Describe what are harmonic fundamental frequencies and
how do we visualize them through nodes and anti node
diagrams.
 Calculate simple fundamental harmonic frequencies for
harmonic vibrations through a tube or down a string?
 Demonstrate that physics laws govern harmonic
frequencies for stringed instruments or open ended
instruments . Can you calculate frequencies an instrument
can produce?
 Do all instruments give the same harmonic frequencies?e
EXIT QUESTIONS ……….
Q1 What type of waves represent sound waves?
How do stationary waves differ from one another?
Q2 What formulas do we use in physics to determine
harmonic open ended or stringed instruments?
Q3 What do you actually need to measure to determine
the harmonic frequency of a wave?
Hand in your calculation for your check for understanding
by en