Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Sound having frequencies above the range of human hearing (about 20,000 Hz) is called \(ultrasound\). Waves above this frequency can be used to penetrate the body and to produce images by reflecting from surfaces. In a typical ultrasound scan, the waves travel through body tissue with a speed of 1500 m/s. For a good, detailed image, the wavelength should be no more than 1.0 mm. What frequency sound is required for a good scan?

Short Answer

Expert verified
A frequency of 1.5 MHz is required for a good ultrasound scan.

Step by step solution

01

Understand the Relationship Between Speed, Frequency, and Wavelength

The speed of a wave, its frequency, and its wavelength are related by the equation \( v = f \lambda \), where \( v \) is the speed of the wave, \( f \) is the frequency, and \( \lambda \) is the wavelength.
02

Identify the Known Quantities

We know the speed of the ultrasound wave in the body tissue is 1500 m/s and the wavelength for a good image is 1.0 mm, which is 0.001 meters.
03

Rearrange the Formula to Solve for Frequency

We need to find the frequency, \( f \). Rearrange the wave equation to \( f = \frac{v}{\lambda} \).
04

Substitute the Values into the Equation

Substitute the known values into the rearranged equation: \( f = \frac{1500}{0.001} \).
05

Calculate the Frequency

Perform the calculation: \( f = \frac{1500}{0.001} = 1,500,000 \) Hz or 1.5 MHz.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Wave Speed
Wave speed is an essential concept in understanding how waves move through different mediums. It indicates how fast a wave travels from one point to another. Wave speed (\( v \)...), frequency (\( f \)...), and wavelength (\( \lambda \)...) are interconnected. The speed of a wave is calculated by multiplying the frequency by the wavelength: \[ v = f \times \lambda \].
  • For ultrasound waves traveling through the body, the speed is determined by the medium – in this case, body tissue, where it typically measures about 1500 m/s.
  • This speed is essential for accurately timing reflections during diagnostic imaging.
Understanding wave speed helps in calculating other important parameters crucial for ultrasound imaging and numerous other applications in science and technology.
Wavelength
Wavelength is the distance between consecutive points of the same phase on a wave, such as crest to crest or trough to trough. It is a crucial factor in determining the level of detail available in an image.
  • For ultrasound imaging, shorter wavelengths (such as 1.0 mm or 0.001 meters) are preferred as they produce higher resolution images.
  • These shorter wavelengths can penetrate deep into the body, providing detailed insights crucial for medical diagnoses.
By understanding wavelength, we can control the resolution of the images produced, leading to more accurate and detailed ultrasound scans.
Wave Frequency
Wave frequency refers to the number of wave cycles that pass through a given point per second. It is measured in hertz (Hz). In the field of ultrasound imaging, frequency is vitally important.
  • A higher frequency results in a shorter wavelength, which in turn, improves image resolution.
  • For example, in a typical ultrasound scan, to achieve a wavelength of 1.0 mm, a frequency of 1.5 MHz is necessary.
Using the formula \( f = \frac{v}{\lambda} \), we can calculate the frequency needed to achieve the desired image quality. Frequency control allows medical professionals to tailor diagnostic procedures to each patient's needs.
Ultrasound Imaging
Ultrasound imaging is a non-invasive diagnostic tool used widely in the medical field. It uses high-frequency sound waves beyond the range of human hearing to create images of the inside of the body.
  • Ultrasound waves are emitted by a probe and travel through body tissues, reflecting off structures and returning to the probe to form an image.
  • Image clarity and detail depend on controlling wave speed, frequency, and wavelength.
  • Typically, the wave speed in bodily tissues is around 1500 m/s, crucial for timing reflections correctly.
Understanding the principles behind ultrasound imaging helps in improving the diagnosis and treatment of various medical conditions, enhancing patient care.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

On December 26, 2004, a great earthquake occurred off the coast of Sumatra and triggered immense waves (tsunami) that killed some 200,000 people. Satellites observing these waves from space measured 800 km from one wave crest to the next and a period between waves of 1.0 hour. What was the speed of these waves in m/s and in km/h? Does your answer help you understand why the waves caused such devastation?

A strong string of mass 3.00 g and length 2.20 m is tied to supports at each end and is vibrating in its fundamental mode. The maximum transverse speed of a point at the middle of the string is 9.00 m/s. The tension in the string is 330 N. (a) What is the amplitude of the standing wave at its antinode? (b) What is the magnitude of the maximum transverse acceleration of a point at the antinode?

A piano tuner stretches a steel piano wire with a tension of 800 N. The steel wire is 0.400 m long and has a mass of 3.00 g. (a) What is the frequency of its fundamental mode of vibration? (b) What is the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 10,000 Hz?

You are exploring a newly discovered planet. The radius of the planet is \(7.20 \times 10^7\) m. You suspend a lead weight from the lower end of a light string that is 4.00 m long and has mass 0.0280 kg. You measure that it takes 0.0685 s for a transverse pulse to travel from the lower end to the upper end of the string. On the earth, for the same string and lead weight, it takes 0.0390 s for a transverse pulse to travel the length of the string. The weight of the string is small enough that you ignore its effect on the tension in the string. Assuming that the mass of the planet is distributed with spherical symmetry, what is its mass?

(a) A horizontal string tied at both ends is vibrating in its fundamental mode. The traveling waves have speed \(v\), frequency \(f\), amplitude \(A\), and wavelength \(\lambda\). Calculate the maximum transverse velocity and maximum transverse acceleration of points located at (i) \(x = \lambda/2\), (ii) \(x = \lambda /4\), and (iii) \(x = \lambda /8\), from the left-hand end of the string. (b) At each of the points in part (a), what is the amplitude of the motion? (c) At each of the points in part (a), how much time does it take the string to go from its largest upward displacement to its largest downward displacement?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free