Question

In some applications of ultrasound, such as its use on cranial tissues, large reflections from the surrounding bones can produce standing waves. This is of concern because the large pressure amplitude in an antinode can damage tissues. For a frequency of 1.0 MHz, what is the distance between antinodes in tissue? (a) 0.38 mm; (b) 0.75 mm; (c) 1.5 mm; (d) 3.0 mm.

Short answer

(b) 0.75 mm.

Step-by-step solution

Understanding the Concept of Standing Waves

Standing waves are formed when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. In such waves, antinodes represent the points of maximum displacement, where destructive interference can cause high pressure values, potentially damaging tissues.

Identify the Frequency Given

The frequency of the ultrasound wave in this problem is given as 1.0 MHz (Mega Hertz). This is equivalent to 1,000,000 Hz.

Determine the Speed of Sound in Tissue

The speed of sound in human tissues is approximately 1540 m/s. This value is typically used for calculations involving biological tissues.

Calculate the Wavelength

The wavelength (\( \lambda \)) of a wave can be calculated using the formula: \( \lambda = \frac{v}{f} \), where \( v \) is the speed of sound in the medium and \( f \) is the frequency of the wave. Substituting the known values: \( \lambda = \frac{1540 \text{ m/s}}{1,000,000 \text{ Hz}} = 0.00154 \text{ m} \), or 1.54 mm.

Calculate the Distance Between Antinodes

In a standing wave, the distance between consecutive antinodes is half a wavelength. Using the wavelength calculated: Distance between antinodes = \( \frac{1.54 \text{ mm}}{2} = 0.77 \text{ mm} \).

Compare with Given Options

The calculated distance between antinodes is 0.77 mm. Comparing this with the options given: (a) 0.38 mm; (b) 0.75 mm; (c) 1.5 mm; (d) 3.0 mm, the closest match is (b) 0.75 mm.

Key concepts

Standing Waves

Standing waves are fascinating phenomena that occur when two waves of identical frequency and amplitude move in opposite directions, intersecting each other. This intersection causes a unique wave pattern that seems to "stand still" rather than move through the medium. In essence, standing waves are made up of points that do not move at all, known as nodes, and points that move extensively, called antinodes. In medical ultrasonography, standing waves can form in tissues due to the reflection of sound waves off surfaces such as bones, especially when using high frequencies.
In the context of ultrasound applications, standing waves are crucial because where these waves form, pressure can reach high peaks. This is particularly important as excessive pressure at antinodes may lead to tissue damage. It’s essential to understand and control standing waves in medical imaging to prevent unwanted tissue exposure to high pressure.

Pressure Antinodes

In a standing wave, antinodes are the locations where the wave reaches its maximum amplitude. In the context of ultrasound, this can mean significantly high pressures. Think of antinodes as the "loudest" parts of a wave, where sound intensity is at its peak.
This is particularly important in medical uses because high pressure can potentially damage tissues at these points of resistance in the wave. For healthcare professionals and engineers, it's crucial to account for the effects of pressure antinodes to avoid adverse outcomes when using ultrasound technology in diagnostics or treatments.
Generally, the risk of damage is assessed and minimized by optimizing the parameters of the ultrasound, such as frequency, to keep the pressure at antinodes manageable.

Sound Speed in Tissues

The speed at which sound travels through a material is known as the speed of sound. In human tissues, this speed is a pivotal factor in ultrasound imaging. On average, the speed of sound in most human tissues is approximately 1540 m/s. This speed is a result of the properties of tissues, which can be compared to the speed of sound in air (about 343 m/s) and water (about 1500 m/s).
The speed of sound in tissues directly influences the wavelength of the ultrasound waves, which in turn affects the image resolution and quality in medical diagnostics. Knowing this speed allows for accurate calculations of distances and positions of structures within the body during imaging.

Ultrasonic Frequency

Ultrasonic frequency refers to sound waves with frequencies higher than the upper audible limit of human hearing, which is above 20 kHz. However, in medical applications, ultrasound frequencies typically range from 1 MHz to 15 MHz. In this exercise, a frequency of 1.0 MHz is used.
The choice of ultrasonic frequency dramatically affects both the depth of penetration and the resolution in ultrasonic imaging. Lower frequencies (around 1 MHz) are suitable for deeper imaging but with less detail, while higher frequencies (around 15 MHz) offer more detailed images but do not penetrate as deeply.
Balancing frequency is crucial in ensuring the most effective and safe usage of ultrasound in medical diagnostics, especially to prevent problems like the formation of standing waves.

Wave Interference

Wave interference is a fundamental concept in physics, including ultrasound physics, describing the phenomenon that occurs when two or more waves overlap in space. The resulting wave pattern depends on the phase of the intersecting waves: constructive interference leads to increased wave amplitude, while destructive interference reduces it.
In medical ultrasound, interference can impact how waves interact with tissues and their boundaries. Such interactions can lead to patterns like standing waves, highlighting the importance of understanding and controlling the conditions for wave interference. Effective management of wave interference enables better image quality and safety in ultrasound applications.