Embed Size (px)
Citation preview
FIZYKA 3 MICHAŁ MARZANTOWICZ
Wave motion
Frequency and angluar frequency
Parameters:
Wavelength
Frequency
Velocity
FIZYKA 3 MICHAŁ MARZANTOWICZ
Description of wave motion
Running wave (in x axis direction)
v
xtf
2
22
2
2
xv
t
Differential wave equation
Wave vector (wave number)
FIZYKA 3 MICHAŁ MARZANTOWICZ
Classification of waves
Transversal wave: Oscillations are perpendicular to
the wave propagation direction.
Longitudinal wave: oscillations in the same direction
as the wave propagation.
FIZYKA 3 MICHAŁ MARZANTOWICZ
Phase and group velocity
Phase velocity: Phase of the wave (e.g. maximal
displacement) propagates in
space with that velocity
Group velocity: Modulation velocity in space
(usually amplitude modulation)
FIZYKA 3 MICHAŁ MARZANTOWICZ
Dispersion of waves
Dispersion: Phase velocity depends on frequency.
Wave packets are formed of waves with
different frequencies.
The width of a wave packet increases.
FIZYKA 3 MICHAŁ MARZANTOWICZ
Standing wave
Open tube
L=n/4, n is odd number
Closed tube
L=n/2
knots
arrows
Flat waves in opposite directions create a standing wave.
( ) ( )vtxgvtxfy ++
T
txAy
2cos
2sin2
+
x
T
tAy 2sin1
+
x
T
tAy
22sin2 Phase changed during reflection
FIZYKA 3 MICHAŁ MARZANTOWICZ
Acoustic waves in gas
( )tkxstxs m cos),(
( )tkxstxs m sin),(
Wave travelling in the direction of x axis.
FIZYKA 3 MICHAŁ MARZANTOWICZ
Sound velocity
M
RTv
Molar mass
Adiabatic exponent
Bv
Elastic modulus(coefficient of
volume elasticity)
Homogeneous medium:
http://hyperphysics.phy-astr.gsu.edu/
dV
dpVB
Medium density
FIZYKA 3 MICHAŁ MARZANTOWICZ
Sound intensity
S
PI
24 r
PI
Wave intensity Source power
surface
Isotropic emission
22
2
1msvI
Wave velocity
Amplitude
Angular frequency
Medium density
Sound wave intensity
FIZYKA 3 MICHAŁ MARZANTOWICZ
Sound intensity level
Intensity level expressed in
decibel dB:
I0: 10-12 W/m2
FIZYKA 3 MICHAŁ MARZANTOWICZ
Source: auto świat
Rules for sound intensity level
93 dB – gasoline engines
96 dB – diesel engines
Measurement: revolutions at
75%maximal power
Bulldozer (caterpillar)
Bulldozer (wheeled)
Excavator (wheeled)
Power [kW] Level [dB]
Polish regulations
FIZYKA 3 MICHAŁ MARZANTOWICZ
Noise reduction
FIZYKA 3 MICHAŁ MARZANTOWICZ
Active noise reduction
Noise reduction by destructive
wave interference:
addition of „anti-noise” with
opposite phase.
Requires sensors – microphones
and microcontroller.
„Metody aktywne redukcji hałasu” Z. Engel, G. Markiewicz,
L. Morzyński, W.M. Zawieska, Warszawa 2001 CIOP
FIZYKA 3 MICHAŁ MARZANTOWICZ
Intensity and pressure – acoustic waves
Hearing level in air:
pref = 20 µPa (rms)
Wave intensity can be obtained by averaging
multiplication of momentary pressure and momentary
velocity.
Wave velocity in medium
FIZYKA 3 MICHAŁ MARZANTOWICZ
Sound intensity and pressure
Sound intensity decreases with squared distance, but pressure
decreases inversely to the distance. A loud noise can break window
glass from a distance!
FIZYKA 3 MICHAŁ MARZANTOWICZ
Human hearing
Pinna „collects” sound (2-3x)
Tympanic membrane converts
pressure to force
Hammer, anvil and stirrup
„couple” the membrane with inner
ear. Inner ear is filled with liquid
and transfers vibrations to
auditory nerve.
Ear can adjust to intensity.
This mechanism is weaker for an
elderly person!
Źródło: hyperphysics
FIZYKA 3 MICHAŁ MARZANTOWICZ
Loudness: phon
1phon correspondes to 1 dB at 1 kHz
Krzywe Fletchera-Munsona
FIZYKA 3 MICHAŁ MARZANTOWICZ
Ultrasound
FIZYKA 3 MICHAŁ MARZANTOWICZ
Doppler effect
Stand-still observer
Generic case:
The„+” sign means approaching of
observer and source.
Stand-still source
Source is approaching:
vT0
f
v
Tvz 0
00 f
v
f
v
f
v z
Observer hears sound with
higher frequency (shorter
wavelength)
FIZYKA 3 MICHAŁ MARZANTOWICZ
Doppler effect – applications
Doppler radar
Astronomy – distant
stars have shifted
spectrum.
Medicine –
Blood velocity
FIZYKA 3 MICHAŁ MARZANTOWICZ
Shock wave
Source velocity is equal or
higher than sound velocity
(supersonic)
