physics beyond 2000 chapter 10 sound waves. nature of sound wave it is longitudinal. it requires...
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Physics Beyond 2000
Chapter 10
Sound Waves
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Nature of Sound Wave
• It is longitudinal.
• It requires medium for transmission.
• The medium may be gas, liquid or gas.
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Propagation of Sound
• http://www.engr.sjsu.edu/~knapp/HCIROD3D/3D_phys/3D_phys.htm
Compression: region with higher pressure.Rarefaction: region with lower pressure.Each molecules are vibrating about their equilibrium positions.
•http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/waveType/waveType.html
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Frequency of Sound
• Range of audible frequency: 20 – 20 kHz
• Ultrasound: f > 20 kHz
• Infrasound: f < 20 Hz
• Pitch of a sound is high(low) if its frequency is high(low).
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How we perceive sound: our ear
• http://library.thinkquest.org/19537/Ear.html
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Application of Ultrasound
• Ship navigation and fishery : sonar.
• Industry: testing flaw, cleaning surfaces etc.
• Medical use: sonographic examination.
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Intensity and Loudness• Intensity: the intensity of sound at a point is
the energy arriving at unit area per unit time.
• Unit of intensity: Wm-2.
A
PI where P is the power of sound
and A is the area around the point.
XFlow ofsound energy
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Examples
• Example 1
Inversely square law for this example.
• Example 2
Discussion of example 1.
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Logarithmic scale of sound loudness
• We can hear an enormous range of the intensity of sound. It is inconvenient in the judgment of loudness.
• Our ear responds logarithmically to intensity.
↓• Use logarithmic scale for the loudness.
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Intensity level
• Intensity level of a sound :
where I is the intensity of the sound
and Io = 10-12 Wm-2 is the minimum detectable intensity.
• Unit of intensity level: decibal (dB)
oI
Ih 10log.10
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Example 3
• Calculation of intensity level.
• Note that intensity level is not intensity. It is a conversion of intensity to a numerical value which is easy to understand.
• Figure 2 on p.200 shows a conversion table.
• Threshold of pain 120 dB
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Decibel and Distance from the source
• Find the change in sound intensity level Δh if the distance from the source is doubled.
• Δh - 6 dB
X Ysource
r 2r
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Decibel and Power
• Fixed the distance of a point X from the source.
• Double the power of the source.
• What is the change of intensity level at X?
X
r
source
•Δh +3dB
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Examples
• Calculation of change of intensity level:
• Example 4
• Example 5
• Example 6
• Example 7
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Loudness• It is a sensation of the human ear.
• If the intensity level increases by 10 dB, the loudness seems to be doubled.
• Our ear responds logarithmically to intensity.
• Our hearing system responds differently with frequencies.
• Most sensitive between 1 kHz to 5 kHz.
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Curves of equal loudness
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Noise pollution
• Prolonged exposure to 90 dB noise damages the hearing.
• People consistently subject to loud noise tend to be bad-tempered and nervous.
Noise pollution in hong kong:http://home4u.hongkong.com/_H4U/education/secondaryschool/chkca99ngou/Noise/Noise.htm
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Sound proofing
• Use fibreglass
• Resonating-air cavity
• Barriers
• Double-glazing windows.
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The Acoustics of Rooms
• Reverberation time: the time for a sound to die away in a hall/room.
• Desired values for speech is 1.0s to 1.5s, while for music playing is about 2.5 s.
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Speed of Sound
• Sound speed varies with medium.
• Sound may refract.
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Speed of Sound in Gas
where P is the gas pressure
and ρ is the density of the gas.
γis a constant depending on the atomicity of the gas.
γ= 1.4 for air
P
c
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Speed of Sound in Gas
Use PV = nRT and the equation for sound speed in air to show that
mM
RTc
where Mm is the molar mass of the gas
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Speed of Sound in Gas
• The speed is in fact independent on the gas pressure.
• c • c depends on the molar mass of the gas.
• speed of sound in air 340 ms-1
mM
RTc
T
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Measure c (Kundt’s tube)
• A stationary wave is set up in the air column of the tube.
• The centre of the heaps represents a position of node.
• The separation between two adjacent nodes =• c = f. λ
2
1
to signal generator
loudspeakerpiston
λ
glass tube
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Speed of Sound in other media
where E is the Young modulus
and ρ is the density of the medium,E
c
•http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe.html
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Measure the Speed of Sound in Steel
• The hammer sends a compression pulse at X.• The pulse travels to Y and is reflected as a rarefaction
pulse.• The hammer remains in contact with the rod until the
rarefaction pulse is back to X.
d
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Measure the Speed of Sound in Steel
• From the oscilloscope, find the time of contact t.
• c = where d is the length of the rod.t
d2
d
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Doppler Effect• Relative motion between the source and the
receiver would result in an apparent change in the observed frequency of a wave.
• Demonstration:
buzzer is the sourceof sound wave
receiver
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Doppler Effect• The observed frequency is higher when the
buzzer is going towards the receiver.
buzzer is movingtowards the receiver
receiver
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Doppler Effect• The observed frequency is lower when the
buzzer is going away from the receiver.
buzzer is movingaway from the receiver
receiver
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Doppler Effect• Relative motion between the source and the
receiver would result in an apparent change in the observed frequency of a wave.
• f = frequency of the wave emitted by the source.
• fr = the observed frequency of the wave by the receiver.
• c = wave speed
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Moving source and change of wavelength
• http://www.explorescience.com/activities/Activity_page.cfm?ActivityID=45
•http://webphysics.davidson.edu/Applets/Applets.html
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Moving Source• Suppose the the source is moving at steady
speed vs.
• The wave in front of the source decreases in wavelength.
• The wave behind the source increases in wavelength.
vs
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Source moving towards the receiver
• Suppose the the source S is moving towards the receiver A at steady speed vs.
• The wave in front of the source decreases in wavelength.
• The receiver A receives a wave of shorter wavelength and thus higher frequency.
S Avs
c
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Source moving towards the receiver
• In 1 second, the source emits f waves.
• In 1 second, the first wave moves a distance of c.
• In 1 second, the source moves a distance of vs.
• These f waves occupy a distance of c – vs.
the apparent wavelength and frequency are
f
vc sr
and f
vc
cf
sr .
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Source moving away from the receiver
• Suppose the the source S is moving away from the receiver B at steady speed vs.
• The wave behind the source increases in wavelength.
• The receiver B receives a wave of longer wavelength and thus lower frequency.
SB vs
c
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Source moving towards the receiver
• In 1 second, the source emits f waves.
• In 1 second, the first wave moves a distance of c.
• In 1 second, the source moves a distance of vs.
• These f waves occupy a distance of c + vs.
the apparent wavelength and frequency are
f
vc sr
and f
vc
cf
sr .
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Sound from an ambulancehttp://home.a-city.de/walter.fendt/phe/dopplereff.htm
When the ambulance is approaching the person, the observed wavelength is shorter, thus a higher observedfrequency.When the ambulance is receding from the person, the observed wavelength is longer, thus a lower observed frequency.observed frequency
time
f
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An Approximate Relationship
• The source is moving towards the receiver at speed vs.
• If the wave speed c >> vs,
then the Doppler shift f f.
• If the source is moving away, take vs on a negative value.
c
vs
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Examples
• Example 8: Maximum and minimum frequencies.
• Example 9: Maximum change 2.f
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Moving Receiver• The receiver is moving at speed vr towards
or away from the source.
source
wave speed = c
receiver
speed of receiver = vr
source
wave speed = c
receiver
speed of receiver = vr
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Moving towards the source• If the receiver is moving towards the source,
the wave speed relative to the receiver is higher.
• The relative wave speed c’ = c + vr
source
wave speed = c
receiver
speed of receiver = vr
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Moving towards the source• The relative wave speed c’ = c + vr
• The apparent frequency fr =
• fr =
source
wave speed = c
receiver
speed of receiver = vr
rvc
fc
vc r .
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Moving away from the source• If the receiver is moving towards the source,
the wave speed relative to the receiver is smaller.
• The relative wave speed c’ = c - vr
source
wave speed = c
receiver
speed of receiver = vr
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Moving away from the source• The relative wave speed c’ = c - vr
• The apparent frequency fr =
• fr =
rvc
fc
vc r .
source
wave speed = c
receiver
speed of receiver = vr
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Approximate Doppler shift
• If c >> vr
then the Doppler shift f = fc
vr .
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Example 10
• The passenger is in a moving train. So the receiver (the passenger) is moving.
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General Formula for Doppler Effect
• If both the receiver and the source are moving,
fvc
vcf
s
rr ).(
the upper signs for relative approachingand the lower signs for relative departure.
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Case 1
wave speed = c
receiver
speed of receiver = vr
source
speed of source = vs
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Case 2
wave speed = c
source
speed of source = vs
receiver
speed of receiver = vr
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Case 3
wave speed = c
receiver
speed of receiver = vr
source
speed of source = vs
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Case 4
wave speed = c
source
speed of source = vs
receiver
speed of receiver = vr
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General Formula for Doppler Effect
• If both the receiver and the source are moving,
fvc
vcf
s
rr ).(
In general, if the source and the receiver move towards each other, a higher pitch is heard.fr > f.
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General Formula for Doppler Effect
• If both the receiver and the source are moving,
fvc
vcf
s
rr ).(
In general, if the source and the receiver move away from each other, a lower pitch is heard.fr < f.
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General Formula for Doppler Effect
• If both the receiver and the source are moving,
fvc
vcf
s
rr ).(
•If the relative speed between the source and thereceiver is v and v << c,
fc
vf .
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Example 11
• Part 1 uses the general formula
• Part 2 uses the approximate method.
• The difference < 0.01 kHz
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Discussion
• 1. Moving source towards the receiver
• vs = c
• 2. Moving source towards the receiver
• vs > c
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Discussion
• 1. Moving receiver away from the source
• vs = c or
• vs > c
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Doppler Effect for EM waves
• The speed of EM wave c >> vr or vs
• We may take the approximation
where v is the relative speed of the source and
the receiver.
fc
vf .
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Example 12
• This will be discussed in more detail at a later stage after studying the emission of line spectrum in chapter 19.
• The result supports the kinetic theory of gas that gas molecules are in random motion.
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Red shift
• Studying the EM waves emitted by stars far away shows that all the frequency becomes lower.
• The result is known as red shift.
• It implies that all stars are moving away from the earth.
Supplementary work
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Example 13
• 1 nm = 10-9 m
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The Big Bang Theory
• All stars are moving away. The universe is expanding.
• There was a starting point for the universe to expand.
• All masses concentrate at a point.• The point exploded and the universe started
to expand.• It is known as the big bang theory.
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Discussion
• Why is it important to observe the far away stars?
• Observe the history!
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Moving reflector
• When a plane mirror is moving at v towards a fixed object, the image moves at 2.v towards the object.
object
v 2v
plane reflector
image
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Moving reflector
The wave seems to come from an image (thesource) which is moving at 2.v towards the receiver.
transmitter
receiver
v2v
reflector
image oftransmitter
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Moving reflector
transmitter
receiver
2v
image oftransmitter
This is a case of moving source and the wavespeed is much higher than the speed of the source.Use approximation,
fc
vf .
2
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Example 14
• Radar speed check.
• As the Doppler shift is very small, it is impossible to measure it directly.
• Use beat frequency to find the Doppler shift.
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Diffraction of sound
• Diffraction of waves depends on the relative sizes of wavelength and the source.
D
D
sin
Angle of diffraction for a rectangular source
source
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Diffraction of sound
• Diffraction of waves depends on the relative sizes of wavelength and the source.
D
D
22.1sin
Angle of diffraction for a circular source
source
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Diffraction of sound
• Diffraction of waves depends on the relative sizes of wavelength and the source.
D
Angle of spread = 2.
source
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Example 15
• Sound of high pitch diffracts less than the sound of low pitch.
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Hi-fi system
• It is designed to have similar angular spread for sound of high pitch and low pitch.
• Use smaller loudspeaker (tweeter) for sound of high pitch.
• Use larger loudspeaker (woofer) for sound of low pitch.
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Interference between two waves
• http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/waveInterference/waveInterference.html
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Interference of sound
• Demonstration of interference of sound
connected to signal generatorphase controller
loudspeaker loudspeaker
The phase controller can change the phase difference between the sounds from the two loudspeakers.
D 2.5
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Interference of sound
• Demonstration of interference of sound
connected to signal generatorphase controller
loudspeaker loudspeaker
Keep both sounds in phase at frequency 850 Hz.What is the separation D? What is the angular spread?
D 2.5
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Interference of sound
• Demonstration of interference of sound
connected to signal generatorphase controller
loudspeaker loudspeaker
Walk in front of the loudspeakers. There will be about 5 positions of maximum.
D 2.5
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Interference of sound• Along the central line, there is constructive
interference.
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Interference of sound
• Switch the phase controller so that the sounds from the loudspeakers are in anti-phase.
• The interference pattern is reversed.
• Along the central line, there is destructive interference.
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Interference of sound
• The interference pattern is reversed.• Along the central line, there is destructive
interference.
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Order of interference m• Along the central line, the order m = 0.
m=0m=1m=1
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Path difference
• The path difference at a point P
= |PS1 – PS2|
• We may express the path difference in terms of the wavelength .
e.g. = m.
S1 S2
P
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Find the highest order m
• For constructive interference, the path difference
= m.
S1 S2
P
a
The two sources are in phase
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Find the highest order m• For constructive interference, the path difference
= m. • The highest order of m occurs at the far end of the
two sources. The maximum path difference
max a
S1 S2 Pa
The two sources are in phase
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Find the highest order m
• a m. m
• The highest order is the integral part of
a
a
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Discussion
• The highest order is the integral part of a
1. a < no line of cancellation2. a = m = 13. a >> too dense to observe
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Standing Waves and Musical Instrument
• Three kinds of musical instruments:– hammered instruments: drum– stringed instruments: piano, guitar, violin etc.– wind instruments: flute, trumpet, saxophone.
• Standing wave is set up in the vibrating elements of the instruments.
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Quality of sound
• Different instruments have their own quality of sound.
• It is determined by the relative amplitudes of the various harmonics.
• Tuning fork produces a fundamental without any harmonics.
Fourier series:http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/sound/sound.html
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Pitch of sound
• The pitch of sound is usually determined by the fundamental frequency.
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Electronic music
• Electronic synthesizer.
• MIDI: Musical Instrument Digital Interface.
http://arts.ucsc.edu/EMS/Music/tech_background/MIDI/MIDI.html
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Stringed Instruments
• Various stationary waves are set up in the string.
• The two ends of the string are nodes
• Strings with different mass and length are for different notes.
• The sounding board is to amplify the sound..
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Stringed Instruments• The two ends of the string are nodes.
• Harmoncis:
fundamental1st harmonic
1st overtone2nd harmonic
2nd overtone3rd harmonic
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Example 16
• Use for the tension.
• The entire length is set into vibration:
T
c
2
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Wind instruments
• open pipe
• close pipe
vibratingelement
open end
vibratingelement
closed end
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Wind instruments
• Various stationary waves are set up in the air column in the pipe.
• An anti-node is formed at the open end.
anti-node anti-nodenode
fundamental
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Wind instruments
• Various stationary waves are set up in the air column in the pipe.
• A node is formed at the closed end.
anti-node node
fundamental
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Open Pipes
fundamental1st harmonic
1st overtone2nd harmonic
2nd overtone3rd harmonic
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End correction
• In practice, the anti-node is at a position slightly outside the tube.
• The small separation between the anti-node and the mouth of the tube is called the end correction e.
• For an open tube, both ends have end correction.
lengthof the tube
e e
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Example 17
• The fundamental is of the lowest frequency.
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Closed pipes
• A node is always formed at the closed end.
fundamental1st harmonic
1st overtone2nd harmonic
2nd overtone3rd harmonic
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End correction
• For a closed tube, only one end has end correction.
e
length of the tube
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Examples• Example 18
The fundamental is the note with the lowest frequency.
• Example 19
closed end node
open end anti-node
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Making sound from a bar• Tap the steel bar with a hammer at one end.
• The microphone can receive a pure sound at the other end.
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Making sound from a bar
• A longitudinal wave is reflected back and forth along the steel bar and a stationary wave is set up. At both ends, there are anti-nodes.
length of the rod
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Making sound from a bar
• The frequency of the sound emitted is also f.
• The wavelength of the sound is
bbc
c
f
c .
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Making sound from a bar
• The frequency of the wave inside the bar is
where cb is the wave speed in the bar
and b is the wavelength of the wave in the bar with b = 2.
.2b
b
b ccf