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**(i) Wavelength at 5 MHz: 0.31 mm**
**(ii) Wavelength at 50 kHz: 31 mm (100 times longer than at 5 MHz)**
**(iii) Advantages of High-Frequency Ultrasound:**
- **Higher Resolution:** Better detail for small structures.
- **Enhanced Contrast:** Clearer images of tissues.
- **Superficial Imaging:** Effective for imaging structures near the body's surface.
- **Reduced Artifacts:** Minimizes imaging issues for clearer images.
These advantages make high-frequency ultrasound ideal for precise medical diagnostics.
Solución
Certainly! Let's address each part of your question step by step.
---
### **(i) Calculating the Wavelength of Ultrasound in Soft Tissue**
**Given:**
- **Frequency (f):** 5 MHz \( = 5 \times 10^6 \) Hz
- **Speed of Ultrasound in Soft Tissue (v):** \( 1550 \, \text{m/s} \)
**Formula:**
The wavelength (\( \lambda \)) of a wave is related to its speed and frequency by the equation:
\[
\lambda = \frac{v}{f}
\]
**Calculation:**
\[
\lambda = \frac{1550 \, \text{m/s}}{5 \times 10^6 \, \text{Hz}} = \frac{1550}{5 \times 10^6} = 0.00031 \, \text{meters}
\]
**Convert to Millimeters:**
\[
0.00031 \, \text{meters} = 0.31 \, \text{mm}
\]
****Answer:**
The wavelength of the ultrasound is **0.31 millimeters**.
---
### **(ii) Wavelength When Frequency is Reduced to 50 kHz**
**Given:**
- **New Frequency (f’):** 50 kHz \( = 50 \times 10^3 \) Hz
**Formula:**
Using the same wavelength formula:
\[
\lambda' = \frac{v}{f'}
\]
**Calculation:**
\[
\lambda' = \frac{1550 \, \text{m/s}}{50 \times 10^3 \, \text{Hz}} = \frac{1550}{50 \times 10^3} = 0.031 \, \text{meters}
\]
**Convert to Millimeters:**
\[
0.031 \, \text{meters} = 31 \, \text{mm}
\]
**Comparing Wavelengths:**
\[
\frac{\lambda'}{\lambda} = \frac{31 \, \text{mm}}{0.31 \, \text{mm}} = 100
\]
****Answer:**
When the frequency is reduced to 50 kHz, the wavelength becomes **100 times longer** than at 5 MHz.
---
### **(iii) Advantages of Using High-Frequency Ultrasound for Medical Diagnosis**
High-frequency ultrasound (e.g., MHz range) offers several advantages over low-frequency ultrasound (e.g., kHz range) in medical diagnostic imaging:
1. **Higher Spatial Resolution:**
- **Shorter Wavelengths:** As calculated, higher frequencies produce shorter wavelengths (e.g., 0.31 mm vs. 31 mm). Shorter wavelengths allow for finer detail in the images, enabling the detection and differentiation of smaller structures within the body.
2. **Enhanced Image Detail:**
- **Better Contrast:** High-frequency ultrasound provides better contrast between different types of tissues, aiding in the accurate identification of abnormalities.
3. **Superficial Imaging:**
- **Ideal for Shallow Structures:** High-frequency waves are particularly effective for imaging structures that are closer to the surface of the body, such as muscles, tendons, skin, and eyes.
4. **Reduced Penetration Depth (Acceptable Trade-off):**
- While higher frequencies have less penetration depth, this is often an acceptable trade-off in diagnostic scenarios where high resolution is paramount, and the areas of interest are accessible.
5. **Minimized Artifacts:**
- Higher frequencies can reduce certain types of imaging artifacts, leading to clearer and more accurate representations of internal body structures.
****Summary:**
Using high-frequency ultrasound in medical diagnostics enhances image resolution and detail, allowing for more accurate and precise examinations of superficial and small anatomical structures. This makes it a superior choice for applications requiring fine imaging compared to low-frequency ultrasound.
---
**Overall Conclusion:**
1. **Wavelength at 5 MHz:** 0.31 mm
2. **Wavelength at 50 kHz:** 100 times longer (31 mm)
3. **Advantages of High-Frequency Ultrasound:** Provides higher resolution and better image detail, enabling more accurate medical diagnostics for superficial and small structures.
Revisado y aprobado por el equipo de tutoría de UpStudy
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