5 (i) Calculate the wavelength of ultrasound travelling in soft tissue if the frequency of the sound is 5 MHz and its speed in the soft tissue is \( 1550 \mathrm{~m} \mathrm{~s}^{-1} \). (ii) How many times as long will the wavelength be if the frequency were reduced to 50 kHz ? (iii) Hence describe the advantages of using high-frequency ultrasound for ultrasound scanning in medical diagnosis instead of low-frequency ultrasound.

Sure, let's address each part of the problem step by step. --- ### **Part (i): Calculating the Wavelength** **Given:** - **Frequency (\( f \))** = 5 MHz = \( 5 \times 10^6 \) Hz - **Speed of sound in soft tissue (\( v \))** = 1550 m/s **Formula:** The wavelength (\( \lambda \)) of a wave is given by the relation: \[ \lambda = \frac{v}{f} \] **Calculation:** \[ \lambda = \frac{1550 \, \text{m/s}}{5 \times 10^6 \, \text{Hz}} = \frac{1550}{5,000,000} \, \text{m} = 0.00031 \, \text{m} \] **Converted to Millimeters:** \[ 0.00031 \, \text{m} = 0.31 \, \text{mm} \] **Answer:** The wavelength of the ultrasound is **0.31 millimeters**. --- ### **Part (ii): Effect of Reducing Frequency to 50 kHz** **Given:** - **New Frequency (\( f' \))** = 50 kHz = \( 50,000 \) Hz **Formula:** \[ \lambda' = \frac{v}{f'} \] **Calculation:** \[ \lambda' = \frac{1550 \, \text{m/s}}{50,000 \, \text{Hz}} = \frac{1550}{50,000} \, \text{m} = 0.031 \, \text{m} \] **Converted to Millimeters:** \[ 0.031 \, \text{m} = 31 \, \text{mm} \] **Comparing to Original Wavelength:** \[ \text{Factor Increase} = \frac{31 \, \text{mm}}{0.31 \, \text{mm}} = 100 \] **Answer:** If the frequency is reduced to 50 kHz, the wavelength becomes **100 times longer** than the original wavelength. --- ### **Part (iii): Advantages of Using High-Frequency Ultrasound in Medical Diagnosis** **High-Frequency Ultrasound Characteristics:** - **Shorter Wavelengths:** As seen in parts (i) and (ii), higher frequencies result in shorter wavelengths. - **Better Spatial Resolution:** Shorter wavelengths allow the ultrasound to detect smaller structures and provide finer detail in the images. - **Shallower Penetration Depth:** While high-frequency ultrasound offers better resolution, it doesn't penetrate as deeply into tissues as low-frequency ultrasound. **Advantages:** 1. **Enhanced Image Clarity:** High-frequency ultrasound can distinguish between closely spaced anatomical structures, making it ideal for detailed examinations. 2. **Improved Detection of Small Lesions:** The ability to resolve smaller features aids in the early detection and characterization of tumors or cysts. 3. **Superficial Imaging:** Best suited for imaging organs and tissues that are close to the skin surface, such as the thyroid, breast, and musculoskeletal system. 4. **Better Visualization of Fine Structures:** Enables clinicians to assess intricate anatomical details like blood flow, nerve structures, and microvasculature. **Conclusion:** Using high-frequency ultrasound in medical diagnostics offers superior image resolution, allowing for more accurate and detailed assessments of superficial tissues and structures. This enhanced clarity is crucial for early detection, precise diagnosis, and effective monitoring of various medical conditions. ---