Mr. DelGiudice Honors Physics. Do Now Complete in next 5 min Define what wavelength and amplitude of...
Preview:
Citation preview
- Slide 1
- Mr. DelGiudice Honors Physics
- Slide 2
- Do Now Complete in next 5 min 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.
- Slide 3
- 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 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?
- Slide 4
- Frequencies Video
- Slide 5
- What is a Standing Wave? What are their characteristics ?
- Slide 6
- 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.
- Slide 7
- 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.
- Slide 8
- 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)
- Slide 9
- What is a Standing Sound wave again? A Sound wave Is a movement
of a wave causing compressions and expansions of molecules
longitudinally. Its source is that of simple harmonic motion It has
a fundamental frequency, f ; a wavelength, 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
- Slide 10
- Slide 11
- Nodes and antinodes describe allowable frequencies
- Slide 12
- Nodes and anti nodes Make up standing waves
- Slide 13
- 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
- Slide 14
- Slide 15
- What are harmonic frequencies? Demo.. Alex, Alexie, Dawn Guitar
Del : Clarinet, Guitar,Harmonica
- Slide 16
- Listen to the harmonic sounds.. 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?
- Slide 17
- Octaves are pairs of the Harmonic frequency Series The 1st
harmonic and the 2 nd 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 of a fundamental frequency
- Slide 18
- Harmonic frequencies what are they? What physics laws predict
them? ?
- Slide 19
- Slide 20
- Slide 21
- Harmonic Frequencies
- Slide 22
- How are sound waves produced again? Listen to the instruments.
DR D.. Alex, Alexie, Dawn others? Answers??
- Slide 23
- 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?
- Slide 24
- What are nodes and anti nodes again? They represent maximum and
minimum????????? Amplitudes!!
- Slide 25
- Nodes and anti Nodes For Open end or Stringed Closed at one end
Displacement anti nodes at both ends Must have at le have at least
one length to have wave at all. Single node corresponds to f1. L =
1/2 or = 2L f n = n v/2L v = speed of sound in air F n=2 = 2 v/2L=
v/L = 2L All integers allowable n= 1,2,3 ex flute Displacement node
always at closed end Anti node at open end L = /4( 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
- Slide 26
- f
- Slide 27
- 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? f 1 = 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 =
- Slide 28
- 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? f 1 = 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
- Slide 29
- 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= ?
Challenge!!! Go for it!!!!!! Prize Time!!!!! By end of class
- Slide 30
- String Lengths
- Slide 31
- For the stringed or open ended harmonic frequencies n = 1 1 = 2
L F 1 n = 2 2 = L 2 F 1 = F 2 n = 3 2 = 2L/3 3 F 1 = F 3 n = 4 2 =
1L/2 4 F 1 = F 4
- Slide 32
- Slide 33
- How many antinodes and nodes are there for the 3 nd harmonic
frequency? For the 5 th ?
- Slide 34
- Now can we measure Harmonic Frequencies? How?
- Slide 35
- Open-end or stringed harmonic frequency formula f = v frequency
times wavelength = velocity Since for an open ended pipe or
stringed instrument : f = v since = 2L here L is length in m f = v
for fundamental frequency 2L
- Slide 36
- For Closed at one end pipes frequencies are odd! f = v
frequency times wavelength = velocity Since for an closed ended
pipe instrument since = 4L here L is length in m f = v since = 4L
here L is length in m f = (n ) v for fundamental frequencies 4L n =
1,3,5,7, only odds
- Slide 37
- 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) ?
- Slide 38
- Look at hand out: Harmonics for AP Music/Physics Theory!!
Listening?
- Slide 39
- String Measurement
- Slide 40
- 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 our desks. Can You Measure Harmonic Frequencies of Instruments
?
- Slide 41
- 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 1 Can you measure the fundamental frequency( n=1) of a
flute with all holes closed?
- Slide 42
- 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
- Slide 43
- 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!
- Slide 44
- Work Station # 4 YOURE 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
- Slide 45
- Look at hand out: Harmonics for Theory
- Slide 46
- Its 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
- Slide 47
- 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 EXIT QUESTIONS .