Ultrasonic waves of frequency 4.5 MHz are used to detect tumour in soft tissues. The speed of sound in tissue is `1.5 km s^-1` and that in air is `340 m s^-1`. Find the wavelength of this ultrasonic wave in air and in tissue.

Explanation

To find the wavelength of ultrasonic waves in air and in tissue, we can follow these steps:

### Step 1: Understand the Given Data
- Frequency of the ultrasonic wave (ν) = 4.5 MHz = \(4.5 \times 10^6\) Hz
- Speed of sound in tissue (V_tissue) = 1.5 km/s = \(1.5 \times 10^3\) m/s
- Speed of sound in air (V_air) = 340 m/s

### Step 2: Use the Wavelength Formula
The wavelength (λ) of a wave is given by the formula:
\[ \lambda = \frac{V}{\nu} \]
where:
- \(V\) is the speed of sound in the medium,
- \(ν\) is the frequency of the wave.

### Step 3: Calculate Wavelength in Tissue
Using the speed of sound in tissue:
\[ \lambda_{tissue} = \frac{V_{tissue}}{\nu} = \frac{1.5 \times 10^3 \text{ m/s}}{4.5 \times 10^6 \text{ Hz}} \]
Calculating this gives:
\[ \lambda_{tissue} = \frac{1.5 \times 10^3}{4.5 \times 10^6} = 3.33 \times 10^{-4} \text{ m} \]

### Step 4: Calculate Wavelength in Air
Now, using the speed of sound in air:
\[ \lambda_{air} = \frac{V_{air}}{\nu} = \frac{340 \text{ m/s}}{4.5 \times 10^6 \text{ Hz}} \]
Calculating this gives:
\[ \lambda_{air} = \frac{340}{4.5 \times 10^6} = 7.56 \times 10^{-5} \text{ m} \]

### Final Results
- Wavelength in tissue: \( \lambda_{tissue} = 3.33 \times 10^{-4} \text{ m} \)
- Wavelength in air: \( \lambda_{air} = 7.56 \times 10^{-5} \text{ m} \)