Properties of sound


Sound waves are very different from electromagnetic (EM) radiation. 

Sound waves X-rays
Mechanical energy EM radiation
Requires a medium Can travel in a vacuum
Longitudinal wave (particles in the medium move back and forth parallel to the direction the wave is travelling) Transverse wave: electric and magnetic component oscillating at right angles to each other, and to the direction of propogation
Variable velocity Constant velocity

Anatomy of a soundwave

 

Anatomy of a soundwave

 

As the sound wave passes through material the particles vibrate back and forth. In some areas the particles are close together (compression) and in others they are further apart (rarefaction). A sound wave can also be represented sinusoidally with the peaks and troughs of the wave corresponding to the areas of maximum compression and rarefaction.

Frequency

The audible range for sound waves for humans is 20 to 20,000 Hz. 1 Hz is 1 wavelength per second. Medical ultrasound uses frequencies of 2-18 MHz (1 MHz = 1 million Hz).

Velocity

The velocity of a sound wave is dependent on and constant for the material through which the wave is passing.

c = √ (ƙ / ρ)
where:
c = speed
ƙ = rigidity
ρ = density

 

From the above equation, the speed of the sound wave increases with increasing rigidity and decreasing density. It travels the slowest in air as the material is so compressible that a lot of energy is lost between the particles. The important number to learn is that for soft tissues the speed is around 1540 m/s. Ultrasound machines are calibrated to this speed to give the best images of soft tissues.

Material Speed of sound (m/s)
Air 330
Water 1480
Tissue 1540
Bone 4080

Wavelength

One wavelength is the distance between two identical points in the wave cycle i.e. the distance between the point of peak compression and the next peak compression. The wavelength is inversely proportional to the frequency but, as the frequency is set by the transducer, it is more often proportional to the velocity of the soundwave.

c = f l
where:
c = velocity
f = frequency
l = wavelength

Intensity

The intensity of a soundwave is measured in watts per metre2 (w/m2). The decibel scale is used to represent the ratio of two intensities.

dB ratio = 10 log10 (I1 / I2)
where:
I1 = intensity one
I2 = intensity two

 

If the attenuation coefficient is 1 dB/cm, after travelling through 10 cm of tissue, the intensity will be reduced by 10 dB or a factor of 10. After 20 cm it would be reduced by 20 dB or a factor of 100

 

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Interaction with tissue

 

Interaction of soundwaves with tissues

 

An ultrasound beam interacts with tissue and is attenuated via four mechanisms:

  1. Absorption
  2. Reflection
  3. Refraction
  4. Scatter

1) Absorption

This is the main cause of attenuation. Energy is transferred to the material it is travelling through as heat. The energy of the ultrasound wave decreases exponentially. Higher frequencies are absorbed more rapidly and, therefore, decrease in intensity more quickly.

2) Reflection

 

Echo of an ultrasound

 

This occurs at the interface/tissue boundaries. The amount of reflection depends on the difference between the acoustic impedance (Z) of the tissues at an interface (acoustic impedance mismatch). This is one reason gel is used in ultrasound, to reduce the acoustic impedance mismatch between the transducer and the skin and to minimise the amount of trapped air between the transducer and the skin. This minimises reflection of the soundwave. At a soft tissue-air interface, over 99% of the echo is reflected.

The acoustic impedance is a measure of how easily material allows soundwaves to pass through, the higher the impedance mismatch, the more the wave is reflected:

Acoustic impedance (Z) (kg m-2 s-1) = density x speed of sound in that material

Reflection coefficient (R) = (Z2 - Z1)2 / (Z2 + Z1)2

Highest Z




Lowest Z

Bone
Liver
Blood
Water
Fat
Gas

 

  • Good transmitters:
    • Small light molecules don't need as much energy to move them
    • Stiff bonds as energy travels quicker through stiffer bonds
  • Poor transmitters:
    • Large dense molecules with weak bonds

3) Refraction

 

Refraction and reflection of a beam

 

When an ultrasound wave crosses an interface between two tissue some of the beam is reflected, the rest passes into the material. As the beam passes into the second material, the velocity changes. This causes refraction, or bending, of the ultrasound wave. The angle of refraction depends on the velocity change of the wave after it has crossed the interface.

4) Scatter

 

Scatter of a beam

 

When a soundwave interacts with an object smaller than a wavelength and most of the beam doesn't interact with it the soundwave is scattered. This is in contrast to when objects are larger than the wavelength in which case they are reflected.

Scatter increases when:

  • Increased size of object causing scatter
  • Increased acoustic impedance mismatch

Σ  Summary

Anatomy of a soundwave

  • Frequency
    • The range of sound audible by humans is 20-20,000 Hz
    • Medical imaging uses ultrasound waves of 2-18 MHz
  • Velocity
    • Velocity = √ (rigidity / density)
    • Velocity faster in bone than air
    • 1540 m/s in most soft tissues
  • Wavelength
    • Velocity = frequency x wavelength
    • Wavelength inversely proportional to frequency but frequency set by transducer. Therefore, wavelength proportional to velocity.
  • Intensity
    • Measured in watts/m2
    • Also measured as the attenuation of sound in decibels (dB) which is the log ratio between two intensities

Interaction with matter

Occurs via three mechanisms:

  • Absorption: main mechanism. More quickly absorbed in higher frequencies
  • Reflection: more reflection when higher impedance mismatch. At a soft tissue-air interface, over 99% of the wave is reflected
  • Refraction: change in velocity as beam crosses an interface causes change in angle
  • Scatter: when particle smaller than a wavelength beam scattered in all directions

Next page: Ultrasound machine


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