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:
• 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:
• noise-induced deafness
• 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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