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## Clinical Echocardiography

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Section 1, Chapter 1
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# Physics of ultrasound

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## Basic sound and ultrasound physics

Unlike light waves, which can propagate through vacuum, sound waves can only propagate through a physical medium. This medium may consist of any matter, e.g air, water, metal, or tissue and fluids in the human body. Sound waves arise when a sound source generates mechanical vibrations in the particles of the medium. These vibrations continue to propagate through the medium at the speed of sound, thus forming a sound wave.

A familiar example is human speech. Humans speak by setting their vocal cords in motion. When vocal cords vibrate, they generate vibrations in the surrounding air and these vibrations propagate in the form of a sound wave. If the sound waves encounter a new medium, some sound waves will be reflected while others will transfer the mechanical (pressure) energy to the new medium, which may also start to vibrate (Figure 1). Figure 1. The principle of how sound waves are generated, propagated and reflected. Red waves represent sound waves that are generated when the vocal cords vibrate. Blue waves represent sound waves reflected by the object.

Although sound waves travel through time and space, the particles of the medium do not travel with the sound wave. The particles merely vibrate and transmit the vibrations to neighboring particles in the medium.

Mathematically, sound waves can be described by a sine curve. This curve is characterized by the following variables: wavelength, amplitude, frequency, speed, and direction. The underlying mathematical principles are simple and important to understand. Figure 2 illustrates the wavelength and amplitude of sine curves. Figure 2. Sound waves can be described mathematically as sine curves.

The peaks and lows of the sine curve correspond to the maximum and minimum pressure, respectively, in the medium. This is illustrated in Figure 3.

## Wavelength

Wavelength is defined as the distance between two points (along the sound wave) with equal amplitude (i.e pressure). It is easy to measure the distance between two peaks (maximum) or two lows (minimum). However, the distance between any two points can be measured, provided there is no pressure difference between them. In Figure 2, the wavelength is measured as the distance between two peaks.

The wavelength of the sound waves of human speech is between 17 millimeters (mm) and 17 meters (m). The wavelength is indicated in the unit m (meters) and is denoted by the letter λ (lambda).

Note that The International System of Units is used throughout this book. This includes the base units metre (length), kilogram (mass), second (time), ampere (electric current) and Kelvin (temperature). This system is recommended globally.

## Amplitude

Amplitude describes the strength of the sound waves, which corresponds to the height of the sine curve (Figure 2). High amplitude equals loud sound and vice versa. In Figure 2, two sound waves of different amplitudes are demonstrated. Note that amplitude actually describes the pressure difference between the highest and lowest particle density along the sound wave (Figure 3). Loud sound is characterized by large pressure differences along the sound wave, while low sound has small pressure differences along the sound wave. Amplitude is denoted in the unit decibels (dB).

## Frequency

Frequency is the number of wave cycles per second. The unit of frequency, which is denoted by the letter f, is Hertz (Hz). In Figure 2, the two sound waves have different amplitudes and different frequencies. If the right sound wave in Figure 2 was recorded during a second, then the frequency would be 5 Hz (since 5 wave cycles are seen in 1 second). If a sound wave has 1000 Hz, then 1000 wave cycles pass every second.

## Audible sound and ultrasound

The human ear can perceive sound waves with frequencies between 20 Hz and 20,000 Hz (20,000 Hz can also be written as 20 kHz). Sound waves with frequency above 20,000 Hz (20 kHz) can not be perceived by the human ear and these sound waves are called ultrasound. Hence, ultrasound is inaudible to the human ear.

It should be noted that there is a large individual variation in the range of audible sound. The vast majority of humans can not hear sound with frequency above 15 kHz. Younger individuals, however, can hear very high frequencies (sometimes >20 kHz), especially if the amplitude is high.

Ultrasound used for clinical diagnostics, e.g echocardiography, has a frequency of between 2 and 10 million Hz (2-10 MHz), which is far beyond audible sound for humans.

## The speed of sound

The speed describes how fast sound waves propagate through the medium. This speed depends on the density of the medium. Sound waves propagate faster in high-density media. The higher the density, the higher the speed. The speed of sound is approximately 300 m/s in air, and 1540 m/s in the human body (which consists mostly of water). The speed is denoted by the letter c and is indicated by the unit m/s.

## Direction of sound waves

Direction simply describes the direction of sound waves in the medium.

## Mathematical equations

There is a simple mathematical relationship between speed (c), wavelength (λ) and frequency (f):

c = f • λ

According to the formula, the speed of the sound wave is the product of the frequency and wavelength. Using this formula, we can calculate the wavelength (λ) for ultrasound with frequency 3 million Hz (3 MHz), which is used in ultrasound diagnostics:

λ =1540 / 3000000 = 0,000513 meter

0.000513 meters is 0.513 mm (millimeter). Thus, the wavelength of the ultrasound is very short, which is desirable in echocardiography, and ultrasonography in general, because it allows detailed visualization of small structures (i.e the resolution becomes high).

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