A hosptital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in a tissue in which the speed of sound is `1.7 km//s` ? The operating frequency of the scanner is `4.2 MHz`.

Explanation

To find the wavelength of sound in tissue using the given speed of sound and operating frequency, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Speed of sound in tissue (V) = 1.7 km/s
- Operating frequency (μ) = 4.2 MHz

2. **Convert the speed of sound from km/s to m/s:**
\[ V = 1.7 \, \text{km/s} = 1.7 \times 1000 \, \text{m/s} = 1700 \, \text{m/s} \]

3. **Convert the frequency from MHz to Hz:**
\[ \mu = 4.2 \, \text{MHz} = 4.2 \times 10^6 \, \text{Hz} \]

4. **Use the wave equation to find the wavelength (λ):**
The wave equation relates speed (V), frequency (μ), and wavelength (λ) as follows:
\[ V = \lambda \times \mu \]
Rearranging gives us:
\[ \lambda = \frac{V}{\mu} \]

5. **Substituting the values into the equation:**
\[ \lambda = \frac{1700 \, \text{m/s}}{4.2 \times 10^6 \, \text{Hz}} \]

6. **Calculating the wavelength:**
\[ \lambda = \frac{1700}{4.2 \times 10^6} \approx 0.00040476 \, \text{m} \]
Converting this to micrometers:
\[ \lambda \approx 404.76 \, \mu m \]

7. **Final result:**
The wavelength of sound in tissue is approximately **404.76 micrometers (μm)**.