A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating freqency of the scanner is 3.2 MHz. The speed of sound in a tissue is 1.6 km `s^(-1)`. The wavelength of sound in the tissue is a) 0.25 mm b) 0.5 mm c) 0.75 mm d) 1 mm

Options

A. 0.25 mm
B. 0.5 mm
C. 0.75 mm
D. 1 mm

Explanation

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency (f) = 3.2 MHz
- Speed of sound in tissue (v) = 1.6 km/s

2. **Convert Units:**
- Convert frequency from megahertz to hertz:
\[ f = 3.2 \, \text{MHz} = 3.2 \times 10^6 \, \text{Hz} \]
- Convert speed from kilometers per second to meters per second:
\[ v = 1.6 \, \text{km/s} = 1.6 \times 10^3 \, \text{m/s} \]

3. **Use the Wavelength Formula:**
- The formula for wavelength (\(\lambda\)) is given by:
\[ \lambda = \frac{v}{f} \]

4. **Substitute the Values:**
- Substitute the values of v and f into the wavelength formula:
\[ \lambda = \frac{1.6 \times 10^3 \, \text{m/s}}{3.2 \times 10^6 \, \text{Hz}} \]

5. **Calculate the Wavelength:**
- Perform the division:
\[ \lambda = \frac{1.6}{3.2} \times \frac{10^3}{10^6} = 0.5 \times 10^{-3} \, \text{m} \]
- Convert to millimeters:
\[ \lambda = 0.5 \, \text{mm} \]

6. **Select the Correct Option:**
- From the options provided, the correct answer is:
\[ \text{Option b) } 0.5 \, \text{mm} \]

### Final Answer:
The wavelength of sound in the tissue is **0.5 mm** (Option b).

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