# 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 propagation Variable velocity Constant velocity

## Anatomy of a sound wave 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 of 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) i.e. above the range of human hearing.

### 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 and proportional to the velocity of the sound wave. In ultrasound imaging, however, the frequency is set by the transducer so it is mainly the velocity that affects the wavelength.

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

### Intensity

The intensity of a sound wave 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 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 traveling through as heat. The energy of the ultrasound wave decreases exponentially. Higher frequencies are absorbed more rapidly and, therefore, decrease in intensity and are absorbed more quickly.

### 2) Reflection 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 sound wave. At a soft tissue-air interface, over 99% of the echo is reflected.

The acoustic impedance is a measure of how easily material allows sound waves to pass through, the higher the impedance mismatch, the more of the wave that 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 ZLowest Z BoneLiverBloodWaterFatGas

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

### 3) Refraction 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

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

Scatter increases when:

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

Σ  Summary

#### Anatomy of a sound wave

• 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 and proportional to velocity. Frequency set by transducer.
• 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 when beam crosses an interface causing change in angle
• Scatter: when particle smaller than a wavelength beam scattered in all directions

#### Next page: Ultrasound machine

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