Physical and physiological acoustics

Question 1

Physical properties of acoustic waves

Answer 1

-Sound is a mechanical disturbance propagated through a deformable medium and can be transmitted through solids, liquids, and gases but not through a vacuum. -Sound waves are produced by a vibration source of suitable frequency and are transmitted through media by the oscillation of its particles. -They are longitudinal in nature meaning that the media particles oscillate around their equilibrium positions in the direction of wave motion. *In the solid phase, oscillation in the transverse direction and longitudinal direction can occur *Sound waves propagate through different media with different velocities. In gas, velocity of sound = c= sqrt(xp/p) x= Cp/Cv Poissions Constant *Velocity of sound is also dependent on temperature. -This stems from the fact that density =m/v and mass = moles x Molar mass and # of moles is directly proportional to temperature. Thus c is directly proportional to density which is directly proportional to T c= sqrt( xRT/M) In liquid, the velocity sound = C= sqrt (k/p) ***The velocity of sound in air is 344 m/s*** In water and soft tissues velocity of sound is 1400 -1600m/s, and in glass it is 6000 m/s. Thus the speed of sound is fastest in solids. -The wavelength of an accoustic wave λ = c/f c= λf Acoustic amplitude (a) – the amplitude of oscillation of media particles which varies between a max value and 0 a=amaxsin(2πft) Acoustic Velocity – the velocity of the vibrating motion of media particles -Also varies between a maximum value and 0 thus effective accoustic velocity was defined. Effective acoustic velocity Acoustic pressure – due to oscillations of media particles producing periodic changes in the density of the media. These produce periodic changes in the acoustic pressure. Acoustic pressure is in phase with acoustic velocity. Effective accoustic pressure *The effective accoustic pressure is related to the effective accoustic velocity, density of the medium, and velocity of sound by Acoustic impedance (z)

Question 2

Acoustic impedance (z)

Answer 2

Is the measure of the opposition that a system presents to an acoustic flow when an acoustic pressure is applied to it of a plane acoustic wave passing through some medium is defined as the ratio of effective acoustic pressure to the effective acoustic velocity z= Pef/vef = pc z=pV p=denisty v=acoustic velocity of material Zair = 440 pa.s.m-1 unit is pa.s.m-1

*Acoustic impedence is greater in more dense materials

Question 3

Doppler’s effect.

Answer 3

The Doppler effect is the change of frequency or wavelength, observed by an observer, caused by the relative motion of observer or source with respect to the medium. If the observer is at rest and teh source of sound moves with velocity v_source, then:

λ = λ₀ ± (ν_source/f₀) … where… λ₀ = c/f₀ is the wavelength in the case that the source is at rest. Its frequency = f₀ and the waves propagate with velocity c. In general case of movement of the source and of the observer as well, the frequency observed is given by:

f = f₀ (c ± ν_source / c ± ν_detector) where v_detector is velocity of the detector motion with respect to the medium towards the source

v_source is the velocity of the source with respect to the medium towards the detector. This effect is used at the evaluation of the blood flow velocity in blood vessels.

Question 4

Sound intensity and loudness, units

Answer 4

Sound intensity, I - The amount of energy passing through an area of 1m² perpendicular to the direction of wave propagation within 1s (Intensity =P/A)

Units W/m²

I = v_ef P_ef = P²_ef / ρc

*Intensity of sound is directly proportional to the effective accoustic pressure squared.

Intensity Level L (units are the bell or decibel)

In decibels…

L = 10 log I/I_o

In bells…

L = log I/I_o

* If intensity increases by 100, intensity level is 20 dB

Loudness

• Is a physiological quantity that describes the perception of sound.
• Intensity of sound of frequency 16Hz to 16kHz that comes to the ear results in hearing and the perception of sound is described by its physiological quantity loudness.
• Sound perception is subjective and the ear is sensitive to various frequencies to various extents, therefore loudness is NOT proportional to intensity
• The dependence of loudness on the intensity of the stimulus is described by Weber-Ferchner’s Law : the change in loudness (∆L is proportional to the relative change in the stimulus
• Units of Loudness are the phones (ph)

speech is 40-60 phones

Question 5

Field of hearing

Answer 5

The field of hearing is a region of sound intensities and frequencies that induces the effect of hearing.

The field of hearing can be visualized by a graph of frequency (hz) vs. intensity (dB).

Curve of lowest intensity level represents the threshold of hearing. → corresponds to a loudness of 0 DB/ 1khz frequency à 10^-12 W*m^-2

The threshold of pain (130Db) represents the upper boundary of hearing and is virtually

independent of frequency.

Each curve in between represesnts an intensity level of the same loudness and the frequencies at which it occurs.

Between 2 curves can be plotted iso-loudness lines.

Speech = 40-60Ph

street=60-90 Ph

jet=120-130 Ph

*Sound of frequency 16 Hz to 16,000 Hz can be perceived by the human ear

* highest sensitivity of the human ear was detected at frequencies of 1-5 kHz

Question 6

Weber-Fechner´s law

Answer 6

The dependence of loudness on the intensity of the stimulus is described by Weber-Ferchner’s Law : the change in loudness (∆L is proportional to the relative change in the stimulus

Loudness

• Is a physiological quantity that describes the perception of sound.
• Intensity of sound of frequency 16Hz to 16kHz that comes to the ear results in hearing and the perception of sound is described by its physiological quantity loudness.
• Sound perception is subjective and the ear is sensitive to various frequencies to various extents, therefore loudness is NOT proportional to intensity
• Units of Loudness are the phones (ph)

Question 7

Ultrasound generators

Answer 7

• Ultrasound waves have frequencies greater than 20 kHz –these are beyond the frequency that humans can detect.
• Ultrasound waves can be produced by mechanical, magnetic, or piezoelectric generators.
• Piezoelectric generators are important in medicine.
• in piezoelectric generators, suitable materials vibrate due to the actions of a high-frequency alterned electrical field in a liquid medium (oil)
• Piezoelectric generators are capable of producing intensities of 10 W/m².
• The velocity of an ultrasound wave is the same as normal sound but ultrasound has a much higher frequency and thus shorter wavelength. λ = v/f
  eg: determine the wavelength at 1MHz. =1500/(10⁶⁾ is 1.5nm

Question 8

Physical principles or diagnostic use of ultrasound

Answer 8

At the boundary of tissues of different acoustic impedances z, the reflection and refraction of sound waves is observed according to the equation

Due to energy loss, sound waves are weakened in each medium to certain extents

The absorption of ultrasound in gas is much higher than in liquid

• Ultrasound is used in medical imaging to visualize muscles, tendons, and many internal organs
• A piezoelectric generated is used to generate ultrasound waves that are directed into the area to be examined
• a water-based gel is placed between the patient’s skin and the probe to increase the efficiency of sound transmission
• The sound waves are partially reflected from layers between different tissues. Specifically, sound is reflected anywhere there are density changes in the body
• The time taken for echoes to return back to the transducer along with some other parameters are used to create the image .
• An ultrasound produces a reflection signature which reveals details about the inner structure of the medium .
• The effects of ultrasound are
• mechanical* - cavitations
• thermal* – increase the temp within regions ultrasound is absorbed
• electrochemical* – decomposition of some high molecular weight compounds and polymerization
• biological* – structural changes, changes in the permeability of cell membranes and conductivity of nerves, alteration of pH, analgesic effects, etc.
• The biological effects of ultrasound depend on intensity

The intensity of ultrasound for diagnostic purposes must not exceed 1.5 W/m², or irreversible morphological changes may occur.

-Can use ultrasound for pre-natal screening, internal medicine, gynecology.

frequencies >20khz

Question 9

Audiometry

Answer 9

• The testing of hearing is most often carried out by establishing the threshold of hearing, the softest sound which can be perceived in a controlled environment.
• It is typical to do this testing with pure tones by providing calibrated tones to a person via earphones, allowing the person to increase the level until it can just be heard.
• Various strategies are used, but pure tone audiometry with tones starting at about 125 Hz and increasing by octaves, half-octaves, or third-octaves to about 8000 Hz is typical.
• Hearing tests of right and left ears are generally done independently. The results of such tests are summarized in audiograms.

L= 10log I / Io (db)