Sound
Sound:
- sound is a longitudinal compression-decompression wave that travels
through an elastic media
- velocity (c):
- its velocity is dependent on the characteristics of the media, travelling
faster in more dense media:
- velocity = sqrt (elastic modulus / density )
- speed in a gas = sqrt (adiabatic bulk modulus / density) =
sqrt(gammaRT/M)
- adiabatic bulk modulus = gamma * pressure of gas
- gamma = ratio of specific heat at constant pressure to specific
heat at constant volume (for air = 1.40)
- R = universal gas constant; T = absolute temperature & M =
molecular mass of the gas
- thus speed of sound:
- air = 331.5m/sec; eg. lungs, bowel
- hydrogen =
1270m/sec;
- water = 1430m/sec; eg. urine
- soft tissues: fat 1450m/sec; liver 1550m/sec; blood 1570m/sec;
muscle 1585m/sec;
- bone = 4080m/sec;
- iron = 5100m/sec;
- glass =
5500m/sec;
- sound
wave characteristics:
- period (T):
- time taken for a particle in the medium through which the wave is
travelling to make one complete oscillation about its rest position
- nb. one oscillation is also referred to as a cycle
- frequency (f):
- the number of cycles per second performed by the particles in the
medium in response to the wave travelling through it
- expressed in hertz (Hz), where 1Hz = 1 cycle per sec, thus 3MHz =
3 million cycles per sec
- human hearing range 20-20,000Hz
- ultrasound: 1-20MHz
- wavelength (l):
- the distance between two consecutive identical positions in the
pressure wave (eg. between two compressions or between two
rarefractions)
- determined by frequency of the wave and the speed propagation in
the medium
- wavelength = speed / frequency, ie. the higher the frequency, the
shorter the wavelength (as with light)
- amplitude (A):
- maximum variation of an acoustic variable
- a measure of the degree of change within a medium when a sound
wave passes through it & relates to the severity of the
disturbance
- expressed in units that are appropriate for the acoustic variable
considered
- power (W):
- the rate at which work is done, or, the rate of flow of energy
through a given area
- in diagnostic ultrasound:
- energy is contained within a beam, so the power is the rate of
flow of energy through the cross-sectional area of the
beam.
- most machines have power limits
- expressed in Watts
- intensity (I):
- power per unit area
- a source of a given power can have intensity increased by
focussing the beam onto a smaller area in a similar way that a
magnifying glass can focus sunlight to burn wood shavings
- in diagnostic ultrasound:
- expressed in milliwatts per square centimeter
- important in the understanding if bioeffects and safety
- sound
wave effects on a medium:
- sound waves passing through a medium causes the particles within the
medium to oscillate according to the sound
wave characteristics and thus gain heat according to the
energy absorbed by the medium
- also, any body that has the properties of inertia & elasticity may be set
into vibration
- most, but not all, bodies may vibrate in more than one manner, & for
each of these modes of vibration, there is an associated frequency as a set
of standing waves are set up and
in addition to the fundamental frequency produced, there are higher
pitched harmonic frequencies such that their frequency = N * velocity
/ 2* length, where N is a positive integer;
- forced vibration and resonance:
- whenever a vibrating body is coupled to a second body in such a manner
that energy is transferred, the second body is made to vibrate with a
frequency equal to that of the original body resulting in forced
vibration.
- whenever, the coupled body has a natural frequency of vibration equal
to that of the source there is a condition of resonance.
- under this condition, the vibrator releases more energy with time,
& the vibration of the resonating body is greatly reinforced,
increasing its amplitude & releasing large amounts of energy
- the resonance of the air column of an organ pipe amplifies the
otherwise almost inaudible sound of the vibrating air jet.
- resonance of a loud speaker to certain frequencies would produce
objectionable distortion of speech or music.
- biologic effects of
sound waves:
- ultrasound:
- see also: ASUM
medical safety policy documents
- heating:
- in tissues which absorb sound & relates to intensity
and duration of exposure
- usually not an issue in diagnostic ultrasound except:
- high power settings such as in Doppler spectral mode
should not be used on fetus esp. in 1st TM
- mechanical forces:
- also result from compression of transducer
- streaming:
- passing an ultrasound beam into a flask of water
containing bubbles pushes all bubbles to distal part of beam
- biologic significance is unclear
- cavitation:
- allows formation of bubbles within medium which may be
stable or collapsing
- biologic significance is unclear
- standing waves:
- production of standing waves from reflected waves between
reverberating interfaces such as bone results in more
intense waves
- intracellular effects:
- chromosomes have been shown to switch DNA between their
tails but biologic significance is unclear
- sound within human hearing range:
- effects
of the medium on the sound wave:
- sound attenuation:
- as a sound wave traverses a medium, various factors cause it to
lose energy and therefore undergo a reduction in amplitude and
intensity
- sound waves are attenuated and lose energy by:
- hitting an acoustic interface and thus are:
- partly reflected or scattered
at lower energy depending on the degree of reflection, ie. a
reduction in amplitude and intensity
- partly transmitted into the medium of the interface with
these waves being refracted within
the interface medium
- absorption by the medium
- reflection:
- reflection occurs at interfaces of medium with differing acoustic
impedance (ie. acoustic impedance mismatch), the greater the
mismatch, the greater the proportion of sound reflected
- acoustic impedance:
- a measure of the resistance of a medium to the transmission of
sound
- acoustic impedance (Z) = density of medium x velocity of
sound in medium
- types of reflection:
- specular reflections:
- occur at large, smooth interfaces (eg. walls, in US:
diaphragm, organ margins)
- angle of reflection = angle of incidence
- non-specular
reflections:
- scatter in many directions with amount not being equal in
all directions
- occurs when interface is equal in size to the wavelength
- in US, provides much of the textural information present
in images & is dependent on:
- frequency
- angle of approach
- Rayleigh scattering:
- scatter equal in all directions independent of angle of
incidence
- occurs when interface is much smaller than the wavelength
- in US, is caused by red blood cells & provides signals
for Doppler assessment of
blood flow
- sound waves are reflected from surfaces such as walls, mountains,
clouds or the ground & may produce echoes if reflected back to the
observer if delay is more than 0.1sec (the reverberation time)
- eg. the rolling of thunder is largely due to successive reflections
from cloud & land surfaces
- in diagnostic ultrasound:
- relies on internal organs reflecting the waves back to the
transducer which detect the strength & timing of the
reflected waves
- reflection occurs where the interface is large relative to the
wavelength of the transmitted sound:
- soft tissue/air interface => 99.9% reflected
- soft tissue/bone => 40% reflected
- liver/kidney => 2% reflected (beam must hit interface
at 90deg to allow detection of the reflected wave)
- avoid bone, gas, & air interfaces with soft tissue as
little sound is transmitted which produces shadowing of deeper
tissues
- thus try to use a soft tissue "window" to view
deep structures
- NB. reflected sound coming back to the transducer may also be
further attenuated!
- refraction:
- refraction is the deviation in the path of a beam
- occurs when a wave travels through interfaces of differing speeds
of sound when the angle of incidence to the interface is not 90deg
(see as for optics - refraction
& Snell's law)
- passing into a medium of slower speed results in the transmission
angle being less than the angle of incidence
- sound is refracted towards earth if (and vice versa for opposite
conditions):
- earth surface is colder than the air
- wind is in same direction as the sound
- in diagnostic ultrasound:
- variations in speed between different soft tissue organs is
generally small (up to 10%), but still deviations in the sound
beam of up to 10deg may occur resulting in mis-registration of
the echoes on the display
- sound
absorption:
- transfer of some of the energy of the sound wave to the medium in
which it is travelling
- absorption increases with frequency and produces a heating
effect
- excessive reverberation in rooms can be reduced by the use of
materials in the rooms to absorb the sound
- approx. reverberation time of a room in seconds = 0.049*room volume in
cub.feet/sum(kA)
- where sum(kA) = total absorption of all materials in the room
- k = absorption coefficient of the material
- open window = 1.00; ordinary plaster = 0.034; carpet = 0.20;
wood = 0.03; drapes = 0.40-0.75; marble = 0.01;
- A = surface area in sq. feet
- NB. not satisfactory for very large or very small rooms or rooms
of peculiar shape.
- for a moderate size auditorium, the reverberation time should be
of the order 1-2sec, if too small, the room will sound
"dead", whilst for a work environment, the reverberation
should be as small as possible to reduce stress due to high sound
levels.
- in diagnostic ultrasound:
- thus high frequency transducers cannot be used for deep
structures
- effect
of sound waves on other sound waves:
- interference:
- spacial:
- if a shrill whistle is blown continuously in a room whose walls
are good reflectors of sound, an observer moving around will notice
points where the sound is exceptionally loud & others where it
is unusually faint.
- temporal:
- if two sets of sound waves of slightly different frequency are
sent through the air at the same time, they will create a resultant
pulse wave which will have a regular swelling & fading of sound,
a phenomenon called beats.
- effect
of motion on the sound wave:
- the Doppler effect:
- if there is relative motion between the source of sound & the
observer, then the frequency of the sound as heard by the observer will
be higher as the object approaches (as here the sound waves in front of
the moving object are being compressed and thus shorter wavelength
& thus higher frequency) & conversely, lower as it recedes:
- observed frequency = (V - vm - vo)/(V + vm
- vs)] * source frequency
- V = velocity of the wave relative to the medium
- vm = velocity of the medium relative to the ground
(this allows for moving medium such as wind)
- vo = velocity of the observer relative to the
ground
- vs = velocity of the source relative to the
ground
- also if medium velocity and observer velocity = zero:
- Doppler shift frequency = 2 x sound source motion velocity
x source sound frequency x cos(z) / speed of sound
- where z = angle between line from observer to source and
the direction of motion of source
- in diagnostic ultrasound:
- source sound frequency here is the transmitted sound
frequency which is then reflected off the moving acoustic
interface (eg. RBC's in a blood vessel)
- it is thus important that maximum Doppler effect will be
seen if the beam is angled away from perpendicular to the
line of motion of the moving interface (ie. away from
perpendicular to a blood vessel)
- when the speed of the source approaches the wave speed, the wave front
is distorted & the above does not hold
- the sonic boom:
- if speed of the source equals the wave speed, the energy piles up in
directions making small angles with the direction of motion, creating
the sonic boom as airplanes pass through the speed of sound,
which is a shock wave and unlike ordinary sound waves & thus the
Doppler effect no longer applies to it. This shock wave is similar to
the bow wave of a boat.
- the sonic boom lasts for as long as the plane is travelling faster
than the speed of sound, not just when it breaks through it.
- this is why the ultra-noisy supersonic Concorde was
unacceptable to most populated countries & could only fly
over oceans making the UK-USA run ideal, but it was too
fuel-thirsty to make a trans-Pacific run.
- when a sonic boom hits the ground, it's called a boom carpet.
This boom carpet is about 1km wide for every 300m of altitude of the
source, so sometimes a plane can be up to 50km away when you hear
the sonic boom.
- not only planes generate sonic booms - a bolt of lightning blasts
through the air at 150km/sec, a lot faster than the speed of sound,
and so you hear a sonic boom - thunder.
- the 1st person to travel faster than the speed of sound (1223kph
at sea level = Mach 1) in a specifically designed craft, in a
relatively safe manner was Charles "Chuck" Yeager in 1947
flying the rocket-powered Bell X-1.
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