Answer
A **longitudinal wave** is a wave where particles move back and forth in the same direction as the wave travels. For the sound wave with a speed of 3 m/s and a wavelength of 1.0 mm, the period is approximately 0.000333 seconds (333 microseconds). Ultrasound imaging uses high-frequency sound waves to create images of internal body structures by detecting echoes reflected from different tissues.
Solution
### 1. Definition of a Longitudinal Wave
A **longitudinal wave** is a type of mechanical wave where the particles of the medium oscillate parallel to the direction of the wave's propagation. In other words, the displacement of the medium's particles is in the same or opposite direction as the wave travels. This oscillatory motion creates regions of compression (where particles are close together) and rarefaction (where particles are spread apart).
**Examples of Longitudinal Waves:**
- **Sound Waves:** Vibrations that travel through air, liquids, or solids.
- **P-waves (Primary Waves) in Seismology:** Travel through the Earth's interior during earthquakes.
### 2. Calculating the Period of the Sound Wave
**Given:**
- **Speed of the sound wave (\( v \))**: \( 3 \, \text{m/s} \)
- **Wavelength (\( \lambda \))**: \( 1.0 \, \text{mm} = 0.001 \, \text{m} \)
**To Find:**
- **Period (\( T \))** of the wave.
**Formulas:**
1. **Wave Speed Equation:**
\[
v = \lambda \times f
\]
Where \( f \) is the frequency.
2. **Period-Frequency Relationship:**
\[
T = \frac{1}{f}
\]
**Step-by-Step Calculation:**
1. **Find the Frequency (\( f \)):**
\[
f = \frac{v}{\lambda} = \frac{3 \, \text{m/s}}{0.001 \, \text{m}} = 3000 \, \text{Hz}
\]
2. **Find the Period (\( T \)):**
\[
T = \frac{1}{f} = \frac{1}{3000 \, \text{Hz}} \approx 0.000333 \, \text{seconds} \, (333 \, \mu\text{s})
\]
**Result:**
The **period** of the sound wave is approximately **0.000333 seconds** or **333 microseconds**.
> **Note:** The speed of sound in air is typically around 343 m/s at room temperature. If the given speed (\( 3 \, \text{m/s} \)) seems unusually low for your context, please double-check the value or its units.
### 3. Creating Images Using Ultrasound
**Ultrasound Imaging**, commonly referred to as **sonography**, is a diagnostic technique that uses high-frequency sound waves to produce images of structures within the body. Here's how it works:
1. **Sound Wave Generation:**
- A device called a **transducer** emits high-frequency sound waves (ultrasound) into the body. These sound waves are typically in the range of 1 to 20 megahertz (MHz), which is above the audible range for humans.
2. **Propagation and Reflection:**
- As the sound waves travel through the body, they encounter different tissues and interfaces (e.g., fluid and soft tissue, soft tissue and bone).
- When sound waves hit different boundaries, some of the waves are reflected back to the transducer, while others continue deeper into the body.
3. **Reception of Echoes:**
- The transducer also acts as a receiver, detecting the reflected sound waves (echoes).
- The time it takes for each echo to return and the strength of the echo are measured.
4. **Image Construction:**
- A computer processes the received echoes to determine the location and intensity of the reflections.
- By scanning the area and collecting data from multiple angles, the system constructs a two-dimensional (2D) or three-dimensional (3D) image of the internal structures.
- The varying intensities of the echoes are represented as different shades of gray on the image, allowing differentiation between tissues.
5. **Real-Time Imaging:**
- Ultrasound can provide real-time images, which are particularly useful for observing moving structures like the beating heart (echocardiography) or monitoring fetal development during pregnancy.
**Advantages of Ultrasound Imaging:**
- **Non-invasive:** No incisions or injections are typically required.
- **No Ionizing Radiation:** Safer compared to X-rays or CT scans.
- **Real-Time Visualization:** Allows dynamic assessment of organ function and movement.
- **Portability:** Devices can be mobile, facilitating bedside examinations.
**Common Applications:**
- **Obstetrics:** Monitoring fetal development.
- **Cardiology:** Assessing heart function.
- **Abdominal Imaging:** Examining organs like the liver, kidneys, and pancreas.
- **Musculoskeletal:** Evaluating muscles, tendons, and joints.
- **Vascular:** Visualizing blood flow in arteries and veins.
**Illustration:**
*Figure: Schematic of Ultrasound Imaging Process*
*Please note that as an AI developed by OpenAI, I cannot provide actual images. The above description is for explanatory purposes.*
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