Find the wavelength of electromagnetic waves of frequency `6xx10^12Hz` in free space. Gives its two applications.

Answer

To find the wavelength of electromagnetic waves with a frequency of \(6 \times 10^{12}\) Hz in free space, we can follow these steps:

### Step 1: Identify the given values
We are given:
- Frequency (\( \mu \)) = \( 6 \times 10^{12} \) Hz
- Speed of light (\( c \)) = \( 3 \times 10^{8} \) m/s

### Step 2: Use the formula for wavelength
The relationship between wavelength (\( \lambda \)), frequency (\( \mu \)), and the speed of light (\( c \)) is given by the equation:
\[ \lambda = \frac{c}{\mu} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ \lambda = \frac{3 \times 10^{8} \text{ m/s}}{6 \times 10^{12} \text{ Hz}} \]

### Step 4: Calculate the wavelength
Calculating the above expression:
\[ \lambda = \frac{3 \times 10^{8}}{6 \times 10^{12}} = \frac{3}{6} \times 10^{8 - 12} = 0.5 \times 10^{-4} \text{ m} \]
This can be rewritten as:
\[ \lambda = 5 \times 10^{-5} \text{ m} \]

### Step 5: Determine the type of electromagnetic wave
The wavelength \( 5 \times 10^{-5} \) m (or 50 micrometers) falls within the range of infrared radiation, which is typically from \( 10^{-4} \) m to \( 10^{-6} \) m.

### Step 6: List two applications of infrared radiation
1. **Physical Therapy**: Infrared radiation is used in physical therapy to treat muscle strains and injuries, as it helps in reducing pain and promoting healing.
2. **Short Range Communication**: Infrared radiation is utilized in remote controls for televisions and other devices, as well as in optical fibers for data transmission.

### Final Answer
The wavelength of the electromagnetic waves with a frequency of \( 6 \times 10^{12} \) Hz is \( 5 \times 10^{-5} \) m, and two applications of infrared radiation are physical therapy and short-range communication.

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