A hospital uses an ultrasonic scanner to locate tumour 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`.

Options

A. `4xx10^(-4)` m
B. `8xx10(-4)` m
C. `4xx 10^(-3)`m
D. ` 8 xx10^(-3)` m

Answer

To solve the problem of finding the wavelength of sound in tissue using the given speed of sound and frequency, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Speed of sound in tissue, \( V = 1.7 \, \text{km/s} \)
- Operating frequency of the scanner, \( f = 4.2 \, \text{MHz} \)

2. **Convert the units**:
- Convert the speed of sound from kilometers per second to meters per second:
\[ V = 1.7 \, \text{km/s} = 1.7 \times 10^3 \, \text{m/s} \]
- Convert the frequency from megahertz to hertz:
\[ f = 4.2 \, \text{MHz} = 4.2 \times 10^6 \, \text{Hz} \]

3. **Use the wave equation**:
- The relationship between speed (V), frequency (f), and wavelength (\( \lambda \)) is given by the equation:
\[ V = f \cdot \lambda \]
- Rearranging this equation to solve for wavelength gives:
\[ \lambda = \frac{V}{f} \]

4. **Substitute the values into the equation**:
\[ \lambda = \frac{1.7 \times 10^3 \, \text{m/s}}{4.2 \times 10^6 \, \text{Hz}} \]

5. **Calculate the wavelength**:
- Performing the division:
\[ \lambda = \frac{1.7 \times 10^3}{4.2 \times 10^6} \approx 0.00040476 \, \text{m} \]
- This can be expressed in scientific notation:
\[ \lambda \approx 4.04 \times 10^{-4} \, \text{m} \]

6. **Final answer**:
- The wavelength of sound in the tissue is approximately:
\[ \lambda \approx 4.0 \times 10^{-4} \, \text{m} \]