Question

Diagnostic ultrasound of frequency \(4.50 \mathrm{MHz}\) is used to examine tumors in soft tissue. \((a)\) What is the wavelength in air of such a sound wave? \((b)\) If the speed of sound in tissue is \(1500 \mathrm{~m} / \mathrm{s}\), what is the wavelength of this wave in tissue?

Short answer

The wavelength of the ultrasound in air is approximately \(0.076 \, \mathrm{m} \) and in tissue, it is approximately \(0.33 \, \mathrm{m}\).

Step-by-step solution

Calculate The Wavelength in Air

First, calculate the wavelength of the ultrasound in air. To do this, use the formula that relates the speed of sound, frequency, and wavelength: \( v = f \lambda \). The speed of sound in air is approximately \( v = 343 \, \mathrm{m/s} \) and the frequency \( f \) is given as \( 4.5 \, \mathrm{MHz} = 4.5 \times 10^{6} \, \mathrm{Hz} \). Rearrange the equation for \( \lambda \) to get \( \lambda = v / f \). Substitute the known values into this equation to calculate the wavelength.

Calculate The Wavelength in Tissue

Second, calculate the wavelength of sound in the tissue. Again, use the wave formula \( v = f \lambda \). This time the speed of sound in tissue (as provided) is \( v = 1500 \, \mathrm{m/s} \), and the frequency is still \( 4.5 \, \mathrm{MHz} = 4.5 \times 10^{6} \, \mathrm{Hz} \). Rearrange the equation for \( \lambda \) to get \( \lambda = v / f \). Substitute the known values into this equation.

Interpret the Results

The results will show that the wavelength is different for the ultrasound in air and tissue. The wave travels faster and thus has a shorter wavelength in tissue. This is crucially important in medical applications, as the difference in wavelengths allows for the production of clear ultrasound images.

Key concepts

Understanding Wavelength Calculation

In ultrasound physics, the concept of wavelength calculation is vital to producing clear and accurate medical images. The wavelength is the distance between consecutive peaks of a wave and is an essential characteristic of sound waves used in medical imaging.
To calculate the wavelength, we use the wave equation: \( v = f \lambda \). Here, \( v \) represents the speed of sound, \( f \) the frequency, and \( \lambda \) the wavelength. Frequencies for medical ultrasound typically range from 1 MHz to 18 MHz.
A higher frequency results in a shorter wavelength, providing detailed images, beneficial in various diagnostic procedures. By rearranging the formula to \( \lambda = \frac{v}{f} \), you can find the wavelength if the speed and frequency are known. This step is crucial in determining how sound waves will interact with different media such as air or tissue. It ensures precise measurements required in medical imaging.

The Speed of Sound in Tissue

The speed of sound varies depending on the medium through which it travels. In tissues, this speed is considerably higher than in air.
For example, while the speed of sound in air is approximately 343 m/s, in soft tissue it is around 1500 m/s. This higher speed is primarily due to the denser composition of tissue compared to air.

• The speed of sound in air is influenced by factors like temperature and humidity, making it less stable than in tissue.
• In tissue, the uniformity and density provide a consistent environment for sound waves, which is why it is a preferred medium in medical imaging.

By using tissue-specific speed values, healthcare professionals can calculate how sound waves will behave when passing through biological material. This results in accurate readings and effective imaging essential for diagnosing patients. The faster speed in tissue also means shorter wavelengths, contributing to higher resolution in medical images.

The Role of Medical Ultrasound Imaging

Medical ultrasound imaging is a widely used diagnostic tool that employs sound waves to visualize internal structures. The principles of sound speed and wavelength are pivotal in generating these high-quality images.
Ultrasound imaging is non-invasive and safely uses sound waves to create images, which is crucial in monitoring fetal development and identifying various medical conditions.

• Higher frequency sound waves produce higher resolution images, which are particularly useful in detecting small objects or details within tissues.
• The variations in speed and wavelength between tissues and other media help in distinguishing between different types of tissues and structures.

Through the precise calculation of wavelengths and understanding of different media's sound speeds, ultrasound technicians can adjust equipment settings to optimize image clarity and diagnostic efficiency.
Overall, understanding these physics aspects ensures the success of medical ultrasound procedures, making it an indispensable technology in modern medicine.