Embed Size (px)
Citation preview
Physics Beyond 2000
Chapter 10
Sound Waves
Nature of Sound Wave
• It is longitudinal.
• It requires medium for transmission.
• The medium may be gas, liquid or gas.
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
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).
How we perceive sound: our ear
• http://library.thinkquest.org/19537/Ear.html
Application of Ultrasound
• Ship navigation and fishery : sonar.
• Industry: testing flaw, cleaning surfaces etc.
• Medical use: sonographic examination.
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
Examples
• Example 1
Inversely square law for this example.
• Example 2
Discussion of example 1.
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.
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
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
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
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
Examples
• Calculation of change of intensity level:
• Example 4
• Example 5
• Example 6
• Example 7
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.
Curves of equal loudness
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
Sound proofing
• Use fibreglass
• Resonating-air cavity
• Barriers
• Double-glazing windows.
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.
Speed of Sound
• Sound speed varies with medium.
• Sound may refract.
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
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
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
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
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
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
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
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
Doppler Effect• The observed frequency is higher when the
buzzer is going towards the receiver.
buzzer is movingtowards the receiver
receiver
Doppler Effect• The observed frequency is lower when the
buzzer is going away from the receiver.
buzzer is movingaway from the receiver
receiver
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
Moving source and change of wavelength
• http://www.explorescience.com/activities/Activity_page.cfm?ActivityID=45
•http://webphysics.davidson.edu/Applets/Applets.html
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
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
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 .
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
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 .
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
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
Examples
• Example 8: Maximum and minimum frequencies.
• Example 9: Maximum change 2.f
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
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
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 .
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
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
Approximate Doppler shift
• If c >> vr
then the Doppler shift f = fc
vr .
Example 10
• The passenger is in a moving train. So the receiver (the passenger) is moving.
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.
Case 1
wave speed = c
receiver
speed of receiver = vr
source
speed of source = vs
Case 2
wave speed = c
source
speed of source = vs
receiver
speed of receiver = vr
Case 3
wave speed = c
receiver
speed of receiver = vr
source
speed of source = vs
Case 4
wave speed = c
source
speed of source = vs
receiver
speed of receiver = vr
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.
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.
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 .
Example 11
• Part 1 uses the general formula
• Part 2 uses the approximate method.
• The difference < 0.01 kHz
Discussion
• 1. Moving source towards the receiver
• vs = c
• 2. Moving source towards the receiver
• vs > c
Discussion
• 1. Moving receiver away from the source
• vs = c or
• vs > c
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 .
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.
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
Example 13
• 1 nm = 10-9 m
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.
Discussion
• Why is it important to observe the far away stars?
• Observe the history!
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
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
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
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.
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
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
Diffraction of sound
• Diffraction of waves depends on the relative sizes of wavelength and the source.
D
Angle of spread = 2.
source
Example 15
• Sound of high pitch diffracts less than the sound of low pitch.
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.
Interference between two waves
• http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/waveInterference/waveInterference.html
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
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
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
Interference of sound• Along the central line, there is constructive
interference.
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.
Interference of sound
• The interference pattern is reversed.• Along the central line, there is destructive
interference.
Order of interference m• Along the central line, the order m = 0.
m=0m=1m=1
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
Find the highest order m
• For constructive interference, the path difference
= m.
S1 S2
P
a
The two sources are in phase
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
Find the highest order m
• a m. m
• The highest order is the integral part of
a
a
Discussion
• The highest order is the integral part of a
1. a < no line of cancellation2. a = m = 13. a >> too dense to observe
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.
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
Pitch of sound
• The pitch of sound is usually determined by the fundamental frequency.
Electronic music
• Electronic synthesizer.
• MIDI: Musical Instrument Digital Interface.
http://arts.ucsc.edu/EMS/Music/tech_background/MIDI/MIDI.html
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..
Stringed Instruments• The two ends of the string are nodes.
• Harmoncis:
fundamental1st harmonic
1st overtone2nd harmonic
2nd overtone3rd harmonic
Example 16
• Use for the tension.
• The entire length is set into vibration:
T
c
2
Wind instruments
• open pipe
• close pipe
vibratingelement
open end
vibratingelement
closed end
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
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
Open Pipes
fundamental1st harmonic
1st overtone2nd harmonic
2nd overtone3rd harmonic
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
Example 17
• The fundamental is of the lowest frequency.
Closed pipes
• A node is always formed at the closed end.
fundamental1st harmonic
1st overtone2nd harmonic
2nd overtone3rd harmonic
End correction
• For a closed tube, only one end has end correction.
e
length of the tube
Examples• Example 18
The fundamental is the note with the lowest frequency.
• Example 19
closed end node
open end anti-node
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.
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
Making sound from a bar
• The frequency of the sound emitted is also f.
• The wavelength of the sound is
bbc
c
f
c .
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
